**SELECTED PUBLICATIONS**

Total number of publications contains more than 400 articles. The list of principal works is given below, divided into sections according to subject.

##### I. Monographs and Monographic Review

- “Diffusion processes and Riemannian Geometry”, Uspekhi Math. Nauk, 1975, 30, 31, pp 3 – 59.
- “Ideas in the theory of Random Media”, Acta Appl. Math, 1991, 12, 139-282, Kluver Acad. Publish.
- “Intermittency, diffusion and generation in a non-stationary Random Medium,” Sov. Sci. Rev.,
**Sec. C, 7**, 1-110, Harvard Acad. Publish. (with Ju Zaldovich, A. Ruzmaikin, D. Sokolov). - “Lectures on probability theory,” 1992 Summer School in probability, Sant-Flour, France, ed. 1994, Springer-Verlag lecture notes, #1581. (with D. Bakry, R.Gill).
- “Parabolic Anderson model and intermittency,” Memoirs of American Math Soc., #518 (with R. Carmona).
- “Topics in statistical oceanography” (lectures), (1995-preprint UNCC), Proceedings of the ONR-conferences (Santa-Monica, 1993, Santa-Barbara, 1994), Stochastic Modeling in Physical Oceanography, Birckhauser, 1996, 343-381.
- “Stochastic Models in Geosystems,” The IMA volumes in mathematics and its applications, Vol. 85, 1997 (editor, together with W. Woyczynski).
- Multiscale averaging for ordinary differential equations,” Homogenization 316-397, Sev. Adv. Math. Appl. Sci, 50, World Sci. Publishing, Niveredge, NJ, 1999.
- “Fluctuations in Chemical Kinetics”, Lecture notes, EPFL, Switerland, 123 pp, 2001.
- Limit theorems for random exponentials”, Preprint NI 03078-IGS, Isaac Newton Institute for Math Sci., 2003, 89 pp (with G. Ben Arous, L. Bogachev).
- “Limit theorems for sums of random exponentials”, Probab. theory related fields, 2005, v 132, 579-612 (with G. Ben Arous, L. Bogachev)
- Transition from the annealed to the quenched asymptotics for a random walk on random obstacles, Annals of Probability, 33 (2005), #6, pp 2149-2187 (with G. Ben Arous, A. Ramirez).
- Geometric characterization of intermittency in the parabolic Anderson model, in Annals of Probability, 35(2007), 439-499(with J. Gartner and W. Kanig).
- Transition from a network of thin fibers to the quantum graphs. Contemp. Math, AMS, 415, 2006, pp 227-239 , Providence, NJ (with B.Vainberg)
- Scattering solutions in networks of thin fibers: small diameter asymptotics., Comm.Math.Phys., 273 (2007), pp 533 – 559 (with B.Vainberg).
- Laplace operator in networks of thin fibers: spectrum near threshold. In Stoch.Analys. in Math Phys., 2209, World Sci., Hackensack, NJ, pp.69 – 93. (with B. Vainberg)
- On the general Zwikel-Lieb-Rozenblum inequalities. In “around the research of Vladimir Maz’ya”, Vol.III, Intern. Math. Ser., Vol.13, Springer, 2009, pp 201 – 246. (with B. Vainberg)
- Book:”Random media in Saint Flour”, Springer, 2012 (with Frank den Hollander and O. Zeituni)
- S.Molchanov, L. Pastur, E. Ray “Examples of Random Schroedinger type operators with non-Poissonian spectra” accepted to Proc. of the conference “mathematical Physics of Disordered System” in honor of L. Pastur (31pp), 2013
- On the mathematical foundation of the Brownian motor theory, in “Journal of Financial analysis”, 267(2014), pp.1725 – 1756 (with L. Koralov and B. Vainberg)
- S. Molchanov (with Ya. Zeldovich, A. Ruzmaikin, D. Sokoloff). Monograph “Intermittency, Diffusion and Generation in a Non-stationary Random Medium”, 2015, Cambridge Scientific Publishers, Reviews in Mathematics and Mathematical Physics, Vol.15, part I (112 pp.)
- “The Dickman – Goncharov distrubution” in “Russian Math Surverys”, Vol 75, #6, 2020 (In Russian), pp. 107-152, English translation 44 pp.
- “On the spectrum of the hierarchical Schrödinger type operator”, In Springer Proceedings in Mathematics and Statistics, Operator Theory and Harmonic Analysis, OTHA 2020, Part II – Probability-Analytical Models, Methods and Applications, https:doi.org/101008/978-3-030-76829-4, pp.43-89., with A. Bendikov, A. Grigoryan

##### II. Markov Processes and Classical Spectral Theory

- On a problem in the theory of diffusion processes, Probab. Theory and Appl., 1964, pp.523-528.
- Some questions in the theory of Martin boundaries., Ph.D. thesis, 80 pp. (in Russian)
- “Martin boundary for invariant Markov processes on a solvable group,” Teor. Veroyatnost. i Primenen., 1967,
**12, No. 2**, 5 pp. - “Martin boundary for a direct product of Markov processes,” Sibirsk. Matem. Zurn., 1970,
**11, No. 2**, 12 pp. - “Diffusion processes and Riemannian geometry,” Uspekhi Mathe. Nauk, 1975,
**30, No. 1**, 57 pp. - “Asymptotic formulas for transition density of the Wiener process in thin tubes,” Demonstr. Math. (Poland), 1982,
**15. No. 3**, 20 pp. (with Yu. Sidorovich).” - “On the class of nilpotent Markov chains. Spectrum of covariance operator,” Markov Proc.Related Fields, 2004, 10, #4, pp.629-652 (with A. Al Hakim, J. Kawsczak).
- “Some Markov chains on Abelian groups with applications,” Random walk and geometry, Berlin, 2004 (with A. Al Hakim).
- “Limit laws for the sums of the products of i.i.d. random variables,” Israel J. Math. , 2005, 148, pp.115 ” 136 (with M. Cranston)
- “Limit theorems with larfe deviations for the Green function of the lattice Laplacian, 2013 (with E. Yarovaya), Izvestuya Rus. Acad. Sci. Vol #76, #4, pp.121-150.
- “Large deviation for the summetric branching random walk on muli-dimensional lattice”, 2013 (with E. Yarovaya), Trudy Steklov Inst. of Math., RAN, Vol. 282, pp. 1-16.
- “Limit Theorems and phase transitions for i.i.d.r.v. depending on parameters” (with M. Grabchak) 2013, Doklady Ran, Vol. 88, 31, pp. 431-434.
- “The size of political club” (with J. Whitmeyer), in Journ. of Math. Sociology, 38(3), 203-218 (2014)
- S. Molchanov (with L.Bogachev and G. Derfel) “Analysis of the archetypal functional equation in the non-critical case”. (M. de Leon et all ed.) In Dynamical Systems, Differential Equations and Applications, AIMS, Springfield MO, 2015 pp.132-141 (doi:10.3934/2015.0132
- S. Molchanov. On bounded continuous solutions of the archetypal equation with rescaling. (with L. Bogachev, G. Derfel) RSPA (Proceedings of Royal Society, A), 471(2015), 20150351, 1 19 (doi:10.1098/rspa 2015, 0351)
- S. Molchanov (with J. Chen and A. Teplyaev). Spectral dimension and Bohr’s formula for the Schrodinger operator on unbalanced fractal space. J. Physics A, Math.Theor, 48 (2015), #39, 22pp.
- S. Molchanov (with J. Whitmeyer). On the kernel of the covariance operator for Markov semigroups. I. Applicable Analysis, 2015 doi.org/10.1080/00036811.2015, 1088522
- S. Molchanov (with E. Yarovaya), The propagating front of the particle population in branching random walk. In New trends in Stochastic Modeling and Data Analysis, Eds. R. Manka, S. McClean, Ch. H. Skiadis ISA ST Athens, Greece (2015), 27 pp.
- S. Molchanov (with M. Grabchak) Limit theorems for two models of i.i.d. random variables with a parameter. Probability theory and applications (2015), Vol.59, # 2, pp.222-243.
- S. Molchanov (with J. Whitmeyer), On the kernel of the covariance operator on Markov semigroups, I. Appl. Anal., 95 (2016), #9, pp.2099-2109, 60J10 (60F05 60J35)
- Brownian motion on AFF (R) and V. Konakov, S. Menozzi. Contemportary Math., Vol. 739, pp. 97-124, #2, 2019

##### III. Classical Spectral Theory

- “Spectral invariants of the Schroedinger operator on the Euclidian torus,” Dokl. Sov. Acad. Sci., 1986,
**286, V. 2**, 5 pp. (with M. Novitzkii). - “Eigenvalue distribution of the Neuman Laplacian or regions and manifolds with gasps,” J. Funct. Anal., 1992,
**108, V. 1**, 5 pp. (with B. Simon and V. Jaksic). - “On spectral asymptotics for domains with fractal boundaries,” (1997), Comm. Math. Physics,
**183**, pp. 85-117 (with B. Vainberg). - “On spectral asymptotics for domains with fractal boundaries of cabbage type,” (1998), Math Phys., Analysis and Geometry, 1, 145-170 (with B. Vainberg).
- “One-dimensional Schroedinger operator with sparse potentials,” preprint, Paris-6,
**No. 111**, 1997, pp. 2-62. Revised version: “Multiscale Averaging for ordinary differential equations. Applications to the spectral theory of 1D Schroedinger operator with sparse potentials,” 1988, “Homogenization”, World Scientific, pp. 316-397. - “Multiscattering on sparse bumps,” 1998, Contemporary Mathem,
**V. 217**, p. 157-181. - “Localization of surface spectra,” Comm. Math. Phys. 208 (1999),
**No. 1**, pp. 153-172. (with V. Jacsic). - “First K&V integrals and absolutely continuous spectrum for 1D Schroedinger operators,” Comm. Math. Phys., 216 (2001),
**No. 1**, 195-213 (with M. Novitski, B. Vainberg). - “Quasi 1D localization: determinis and random potentials,” Markov proc. related fields 9 (2003),
**No. 4**, 687-708. - Slowing down of the wave packets in quantum graphs, Waves Random Complex Media, 15(2005), 101-112 (with B.Vainberg)
- Slowing down and reflection of waves in truncated periodic media, J.Funct.Anal 231(2006), 287-311(with B. Vainberg)
- Scattering solutions in networks of thin fibers: small diameter asymptotics. Comm.Math. Phys. 273(2007), 533-559 (with B. Vainberg).
- Zwikel and quasi-Szeg type estimates for random operators. Comm.Partial Diff.Equations 33(2008), 1033-1047(with J.Holt and O. Safronov)
- Laplace operator in networks of thin fibers: spectrum near the threshold. In “Stochastic Analysis in Mathematical Physics”, 69-93, World Sci. Hackensack, NJ, 2008.
- On the general Zwikel “Lieb ” Rozenblum inequalities, in “Around the research of Vladimir Maz’ya, III”, Intern.Math.Series 13, Springer, 2009, 201-246 (with B.Vainberg)
- “Non-random perturbation of the random Anderson Hamiltonian “. Journal of Spect. Theory, 2011, Vol.1 (2), pp.179-197 (with B.Vainberg)
- “Bargmann type estimates for general Schroedinger operators” (with B.Vainberg), Journal of Math. Sci., 184, #4 ,475-508.
- “On the negative spectrum of the hierarchical Schroedinger operator” (with B. Vainberg), Journ. Funct. Analysis, 163, #9.
- “The structure of the population inside the propagating front with the finite number of the generating centers” (with E. Yarovaya), Doklady Rus. Acad. Sci., mathematics, vol.447, #3, 265-268.
- “Non-random perturbation of Anderson Hamiltonian in 1D case” (with J. Holt, B. Vainberg), Applicable Analysis, 92, #8, 1755-1765
- Intermittency, diffusion and generation in a non-stationary random medium (with A. Ruzmaikin, D. Sokoloff, Ya. Zeldovich), in Cambridge Scientific Publishers, 2015.
- S. Molchanov (with A. Agbor, B. Vainberg). Global limit theorems on the convergence of multidimensional random walk to stable processes. In Stochastic and Dynamics, IS 1550024 (2015), 14pp.
- S. Molchanov (with A. Bendikov, A. Grigoryan, G. Samorodskii). On class of random perturbation of the hierarchical Laplacian. Proceedings of Russian Acad. Sci. (Izvestiya: Mathematics), Vol.79 (2015), #5, pp 859 893.
- Cluster expansion of the resolvent for the Schrodinger operator on non-percolating graphs with applications to Simon-Spencer type theorems and localozation. S. Molchanov, L. Zheng.
- R.Killip, S.Molchanov, and O.Safronov: “One the relation between positive and negative spectra of elliptic operators” Letters Math. Phys, 107 (2017), pp. 1799-1807
- Spectral Analysis of non-local Schroedinger operators. Yu. Kondratiev, S. Molchanov, B. Vainberg, Journal of Functional Analysis 273 (2017), pp. 1020-1048
- “Negative eigenvalues of non-local Schrödinger operators with sign-changing potentials” (with B. Vainberg), Proceedings of AMS, 151, #11, 4757-4770 (2023), arXiv: 2209.12124
- Hierarchical Schrödinger operators with singular potential “(with A. Bendikov and A. Grigorian), 28 pp., accepted in Proceedings of Steklov Institute Matematika, 2023, V.323, pp. 1 – 36

##### IV. Localization Theory

- “A random one-dimensional Schroedinger operator has a pure point spectrum,” Funckcional. Anal. i Prilozen, 1977,
**11, No. 1**, 10 pp. (with I. Goldsheid and L. Pastur). - “The structure of eigenfunctions of one-dimensional unordered structures,” Izv. Akad. Nauk SSST Ser. Mat., 1978,
**42, No. 1**, 34 pp. - “The local structure of the spectrum of the one-dimensional Schroedinger operator,” Comm. in Math. Phys., 1981, 78, No. 3, 17 pp.
- “Spectral properties of the general Sturm-Liouville equation with random coefficients,” Math. Nachr. (DDR), 1982,
**102**, 22 pp. (with H. Seidel). - “On the basic states of one-dimensional disordered structures,” Comm. Math. Phys., 1983,
**90, No. 1**, 23 pp. (with L. Grenkova and L. Sudarev). - “Spectral properties of random operators,” Doctor thesis, 1983, 300 pp.
- “Spectral properties of rare scatterers and counterexamples to Schroedinger and Steklov hypotheses,” Proc. Math. Phys. Congress, England 1989, 15 pp. (with V. Maslov).
- “One-dimensional Schroedinger operator with unbounded potential: pure point spectrum,” Funct. Anal. And Appl., 1990, 3, 24 pp. (with L. pastur, V. Kirsch).
- “One-dimensional Schroedinger operators with high potential barriers,” Operator theory: Advances and Applications, 1992, 57, Birkhauser. (with L. Pastur, V. Kirsch).
- “Lectures on localization theory,” Preprint, Caltech, 1990, 58 pp.
- “Intermittency and localization: new results,” Proceedings of the ICM, Kyoto, Japan, 1990,
**2**. - “Localization at large disorder and extreme energies: an elementary derivation,” Comm. Math. Phys., 1993, 157, 245-278. (with M. Aizenman).
- “Spectral properties of random Schroedinger operator with unbounded potentials,” 1990, Caltech, preprint, (1993), Comm. Math. Phys., 157, 23-150. (with A. Gordon, V. Jaksic, B. Simon).
- “Hierarchical random matrices and operators. Applications to Anderson model,” 1996, Proc. G.E. Lucas Symposium, ed. A. Gupta, V. Girko,
**VSP**, pp. 179-195. - “On the propagation properties of surface waves,” The IMA Volumes in Math and Appl., V. 96, pp. 143-154. (with V. Jaksic, L. Pastur).
- “On the spectrum of the surface Maryland model,” 1998, Lett. In Math. Phys.,
**45**: 185-193. (with V. Jaksic). - “On the surface spectrum in dimension two,” Helv. Phys. Acta 71 (1998), No. 6, pp. 629-657. (with V. Jaksic).
- Spectrum of multi-dimensional Schroedinger operator with sparse potential in “Analytical and computational methods in scattering and applied mathematics,” Newark, DE, (2000), 231-254, Chapman and Hall CRC, 417. (with B. Vainberg).
- Localization for ID long range random Hamiltonians, Rev. Math. Phys, 11 (1999) No. 1, 103-135. (with V. Jaksic).
- “Schroedinger operator with matrix potentials, transition from the absolutely continuous to the singular spectrum,” J. Funct. Anal., 215 (2004), 111-129. (with B. Vainberg).
- “Simplicity of eigenvalues in the Anderson model”. J.Stat.Phys. 122 (2006), 95-99 (with A.Klein).
- “Anderson parabolic model for a quasi-stationary medium” J.Stat.Phys. 129(2007), 151-169 (with C.Boldrighini and A.Peligrinnotti).
- “Quenched to annealed transition in the parabolic Anderson problem” Probab.Theory Related Fields, 138 (2007), 439-499(with M. Cranston).
- “Ljapunov exponent of the random Schroedinger operator with white or short-range correlated noise potential” (with Yu. Godin, B. Vainberg), Russian Journal of Math. Phys., 20 No 4(2013), 438 452 (accepted in 2013 and published in 2013),

##### V. Percolation Theory

- “Percolation theory and its applications,” Itogi Nauki i Tekniki, Moskva: VINITI, 1986,
**24**, 58 pp. (with M. Menshikov and A. Sidorenko). - “Percolation in random fields,” I, II, III, Teoret, i Matem. Fiz., 1983,
**55, No. 2**, 11 pp., 1983,**55, No. 3**, 12 pp., 1986,**67, No. 2**, 9 pp. (with A. Stepanov). - “Multiscale failure and percolation models,” PAGEOPH, 1990,
**V. 61**, 10 pp. (with V. Pisarenko and A. Reznikova). - “Infinite scale percolation in a new model of the global Universe,” Journal of Statistical Physics, 1995, (with A. Mezhlumina).
- “Percolation of level sets for two dimensional random fields with lattice symmetry,” Journal of Statistical Physics, 1995, (with K. Alexander).
- “Diffusion in an annihilating environment”, Nonlinear Anal.Real World Appl. 7(2006), 579-612,(with J. Gartner and F. den Hollander).

##### VI. Averaging, Intermittency, and Diffusion in Random Media

- “Kinematic dynamo in random flow,” Uspekhi Fiz. Nauk, 1985,
**145, No. 4**, 36 pp. - “Intermittency in a random medium,” Uspekhi Fiz. Nauk, 1987,
**152, No.1**, 30 pp. (with Ja. Zeldovich, A. Ruzmaikin, D. Sokolov). - “Ideas in the theory of random media,” Manuscript of a book, deposed in VINITY, 1988,
**No. 9140B88**, 176 pp. (Russian). - “A dynamo theorem,” Geoph. Astrophys. Fluid Dyn., 1986,
**30**, 12 pp. (with A. Ruzmaikin, D. Sokolov). - “Intermittency of passive field in random media,” Zh. Eksp. Teor., Fiz., 1985,
**89**, 12 pp. - “Kinematic dynamo in the linear velocity field,” J. Fluid Mech., 1984,
**144**, 11 pp. (with Ja. Zeldovich, A. Ruzmaikin, D. Sokolov). - “Parabolic problems for the Anderson model. Intermittency and related topics,” Comm. Math. Phys., 1990,
**v.132**, 613-655 (with Ju. Gortner). - “Parabolic equations with a Levy random potential,” Proc. Charlotte Conf. in Stoch. Partial Diff. Equa., Charlotte, N.C., 1992, 25 pp. (with H. Anh and R. Carmona).
- “Intermittency and phase transition for some particle systems in random media,” Proc. Katata Symp., Japan, 1992, 20 pp. (with R. Carmona).
- “Liapunov exponents for a distribution of magnetic field in dynamo model,” The Dynkin’s Festshritt, Progress in Probability, 1994,
**134**, Birkhouser, 287-306 (with A. Ruzmaikin). - “Stationary parabolic and Anderson model and intermittency,” Probab. Theory Relt. Fields 102 (1995), No. 4, 433-453. (with R. Carmona).
- “Reaction-diffusion equations in the random media: localization and intermittency,” IMA Volumes in Math and Appl.,
**V. 77**(1996), pp. 81-109. - “Parabolic problems for the Anderson Model,” II. Second order asymptotics and structure of high peaks (1998), Probability theory Related Fields,
**V. 111**, 17-55 (with J. Gortner). - “Annealed moment Liapunov exponent for a branching random walk in a homogeneous environment,” Markov process Relt. Fields, 2000,
**V. 6**, No. 4, 473-516. (with S. Albeverio, L. Bogachev, E. Yarovaya). - Moment asymptotics and Lifshitz tails for parabolic Anderson model “Stochastic models”, CMS Cont Proceed. 26, AMS, 2000, pp. 141-157. (with Ju. Gartner).
- “Almost sure asymptotics for the continuous parabolic Anderson model,” Prob. Theory Relt. Fields 6, 2000, No, 473-516. (with Ju. Gartner, W. Konig).
- “Asymptotics for the boundary parabolic Anderson model in halt space,” Random operat. Stochastic equat., 12 (2004) No. 2, 105-128. (with R. Carmona, S. Guishin).
- “Limit laws for sums of products of exponentials of i.i.d. random variables”, Israel J. Math 148(2005), 115-136(with M. Cranston)
- “On phase transitions and limit theorems for homo-polymers” in “Probability and Mathematical Physics”, CRM Proc. Lecture Notes 42, 97-112 Amer.Math.Soc., Providence, RI, 2007.
- “Homo-and hetero-polymers in the mean field approximation”, Markov Processes and Related Fields, Vol.15(2009), 2, 205-224 (with M.Cranston and O.Hryniv).
- “Continuous model for homo-polymers”, J.Funct.Anal., 256(2009), 8, 2665-2696(with M.Cranston, L.Koralov and B. Vainberg).

##### VII. Hydrodynamics and Oceanography

- “Variability of temperature field of ocean surface,” DAN USSR, 1985,
**283**, 3 pp. (with A. Ruzmaikin, L. Piterbarg, D. Sokolov). - “Turbulent diffusion of impurities gradients,” DAN USSR, 1985,
**283, No. 5**, 4 pp. - “Generation of the long-scale anomalies of the ocean surfaces temperature by the short period atmosphere processes,” Isv. An. USSR, 1987,
**5**, 7 pp. (with D. Sokolov, L. Piterbarg). - “Localization of Rossby waves,” DAN USSR, 1989,
**306**, 4 pp. - “Heat propagation in random flows,” Russian J. of Math. Phys., 1992,
**v. 1**, 24 pp. (with Piterbarg). - “Stratified structure of the Universe and Burgers equations ” a probabilistic approach,” Probability theory and related fields, 1994,
**100**, 457-484 (with S. Albeverio, D. Surgailis). - “Hyperbolis asymptotics in Burger”s turbulence and extremal processes,” Communications in Mathematical Physics, 1995,
**168**, 209-226 (with D. Surgailis, W. Woyczynski). - “Wiener-Kolmogorov conception of the stochastic organization of Nature,” Proc. Of Norbert Weiner centurary congress, Michigan St. University, 1994, AMS, Proc. Of Symposia in Appl. Math, 1997,
**v.52**. pp. 1-36. - S. Molchanov (with D. Faizullin, I. Nesmelova). Theoreticaland experimental investigation of the translation diffusion of proteins in the vicinity of the temperature-induced unfolding transition,” in the Journal of Physical Chemistry, 120, pp. 10192-10198, 2016.
- “Massive parallel simulation of motions in a Gaussian velocity field,” Stochastic Modeling in Oceanography, Birckhauser, 1996, pp. 47-68 (with S. Grishin, R. Carmona).
- “Large-scale structure of the Universe and quasy-Veronsi tessellation structure of the shock fronts in forced Burger turbulence,” 1997, Ann. Appl. Probab., v 7, 1, pp. 200-228.
- “Asymptotics for a.s. Liapunov exponent for the solution of non-stationary parabolic Anderson problem,” Random Operat. Stoch. Equat. 9(2001) No. 1, 77-86. (with R. Carmona, L. Coralov).
- “Solitone turbulence as a thermodynamic limit of stochastic solution lattice,” Phys D 152/153 (2001), 653-664. (with G. El, A. Krylov, S. Venakides).

##### VIII. Chemistry Kinetics

- “Some properties of the percolation models of polymer aging,” DAN USSR, 1988,
**302, v 3**, 4 pp. (with B. Gnedenko, R. Braginskii, G. Zaitzeva). - “Mathematical models of hierarchical polycrystal structures,” DAN USSR, 1988,
**302, v 4**, 4 pp. (with R. Braginskii, G. Narkunskaja, A. Reznikova). - “Trap correlation influence on Brownian particle death: One dimensional case,” Phys. Letters A, 1992,
**v 161**, 4 pp. (with A. Brezhkovskii, Ja. Makhnovskii, R. Suries, L. Bogachev). - “Trap correlation influence on diffusion-limited process rate,” Phys. Review A, 1992,
**45, v 8**, (with A. Brezhkovskii, Ja. Makhnovskii, R. Suries, L. Bogachev). - “Diffusion-limited reactions with correlated traps,” Chem. Phys. Lett., 1992,
**193, v 4**. - “Brownian particle trapping by cluster of trays,” Phys. Rev. E., 1993,
**v 47**, 6 pp. 4564-4567 (with A. Brezhkovskii, Ja. Makhnovskii, R. Suries, L. Bogachev). - “Correlation effects in trapping problems,” CMS Conference Proceedings Series, Vol. 29, AMS, 2000, pp. 29-42. (with A. Brezhkovskii, Yu. Makhnovskii, L. Bogachev).
- “Fluctuations in chemical kinetics,” Lecture notes, EPFL, Switzerland, 2001.
- S. Molchanov (with D. Faizullin, I. Nesmelova), Theoretical and experimental investigation of the translational diffusion of proteins in the vicinity of the temperature-induced unfolding transition, in the Journal of Physical Chemistry, 120, pp.10192-10198

*IX. Population* Dynamics

- S. Molchanov (wiht J. Whitmeyer). Stationary distribution in KPP-type model with infinite number of particles. Interational Journal on Mathematical Demography, 2015, 24(32), 147-160.
- S. Molchanov (with A. Getaan and B. Vainberg), Intermittency for branching walk with heavy tails, in Stochastic and Dynamics, 2016, Vol. 17, #6, pp. 14
- S. Molchanov (with Yu. Kondratiev, A. Piatnitski, E. Zhizhina, Resolvent bounds for jump generators, in Apllicable Analysis, http://dx.doi.org/10.1080/00036811.2016.1263838 , 2016, pp. 1-14.
- “Stationary distribution in KPP type model with infinite number of particles”. Math Population Studies (Journal Math. Demography) (2015), 24132, 147-160.
- “Global stability in a non-linear reaction-diffusion equation (D. Finekstein, Yu. Kondraticv, S. Molchanov, P. Tkachcv), in Stochastics and Dynamics, 2018, Vol. 5. #5, 1850037, 15 pp.
- “Steady state and intermittency in the critical branching random walk with arbitrary total number of offspring” (E. Chernousova, S. Molchanov), in Mathematics Population studies, 27:1, 47-63, DOI: 10.1080/08898480.2018.1493868
- “Population model with immigration in contunuous space (with. E. Chernousova, Ostap Hryniv), published online 03 July 2019, in Mathematical Population Studies, https://doi.org/10.1080/08898480.20198.16266189
- Probabilistic approach to a cell growth model” (with Yaqin Feng and Gr. Dergel) in Contemporary Mathemaatics, Vol. 734, 2019, editied by P. Kuchment and Evgeny Semenov, Vol. 1, Differential Equations, Mathematical Physics and Applications: Selim Grigorievich Krein Centennial, ISBN: 987-1-04704-3783-1, pp. 95-107.
- “Branching Random Walks with Immigration. Lyapunov Stability” (with Yu. Makarova, D. Han, E. Yarovaya), in Markov Processes and Related Field 25, 983-708 (2019).
- “Popualtion dynamics with moderate tails of the underlying random walk” (with B. Vainberg), SIAM Journ. Math. Anal., 2019, V.51, Issue 3, pp. 1824-1835.
- E. Chernousova, Y. Feng, O. Hryniv. S. Molchanov and J. Whitmeyer, “Steady States of Lattice Population Models with Immigration,” in Mathematical Population Studies https://doi.org/10.1080.00036811.2020.1820998
- Y. Feng, S. Molchanov, E. Yarovaya. “Stability and Instability of Steady States for a Branching Random Walk,” in Methodol. Comput.Appl.Probab (2020) https;//doi.org/10.007/s11009-020-09791-0 May 4, 2020, Springer Science + Business Media, LLC, part of Springer Nature 2020.
- “Wick-Fourier-Hermite Series” (with E. Chernousova and A. N. Shiryaev), in Markov Processes and Related Fields, Issue 4, 459-492, DOI: 10.61102/1024-2953-mprf.2023.29.4.001
- Branching Random Walks with Two Types of Particles on Multidimensional Lattices (with lulia Makarova, Daria Balashova, E. Yarovaya), Mathematics 2022, Volume 10, Issue 6, 46 pp.
- “The conditions of supercriticality for the branching random walks in the random killing environment with the single reproducing center” (with V. Kutsenko and E. Yarovaya), Uspekhi matematicheskikh nauk, 2023, V.78, 5(473), pp. 181-183

##### X. Limit Theorems and Phase Transitions

- S. Molchanov (with M. Grabchak) Limit theorems for two models of i.i.d. random variables with a parameter. Probability theory and apllications (2011=5), Vol. 59, #2. pp. 222-243.
- S. Molchanov (with D. Faizullin, I. Nesmelova), “Theorestical and experimental investigration of the translational diffusion of proteins in the vicinity of the temperature-induced unfolding transition”, in the Journal of Physical Chemistry, 120, pp. 10192-10198.
- “Entropic Moments and Domains of Attraction on Countable Alphabets” (S. Molchanov, Z. Zhang and L. Zheng), in Mathematical Methods of Statistics, 2018, Vol. 27, #1, pp. 6-70, DOI:10.3103/S1066530718010040
- “Limit theorems for random exponentials: the bounded support case” (M. Grabchak, S. Molchanov), in Russian, in Teoriya Veroyatnostei i ee Primeneniya, 2018, V. 63, #4. pp. 779-794, DOI: htpps:dio.org/10.4213/tvp5149
- “Stable limit laws and structure of the sealing function for reaction-diffusion in random environment” (with A. Ramirez and G. Ben-Arous), in “Probability and Analusis in Interacting physical systems”, the Spinger Proceeding in Mathematics and Statistics of the Conference in the honor of S.R.S. Varadhan, 1.1.2019, V. 283, pp. 123-171, DOI 15338-0-510.1007/978-3-030
- “Limit Theorems for Random exponentials. The Bounded Support Case” (with M. Grabchak), Published in Theory of Probability and Its Apllications, 2019, 63(4): 634-647.
- “Limit Theorems for the alloy-type random energy model” (with V. Panov) in Stochastics, Volume 91, Issue 5, pp. 754-772, https://doi.org/10.1080/1744508.2018.1545841
- “On the critical behavior of a homo-polymer model,” (with M. Cranston), in Sci China Math, 2019, Vol. 62, #8, pp. 1463-1476.
- “The alloy model: Phase Transitions and Diagrams for a Random Energy Model with Mixtures” (with M. Grabchak, in Markov Processes Relat. Fields 25, 591-613 (2019).
- L. Koralov, S. Molchanov, B. Vainberg. “On the Near-Critical behavior of Continuous Polymer,” in Israel Journ. Function. Anal., accpeted Oct. 11,2020.
- L. Koralov, S. Molchanov, B. Vainberg. “The Radius of a Polymer at a Near Critical Temperature, in Applicable Analysis”; accepted Sept., 2020.
- Around the Infinite Divisibility of the Dickman Distribution and Related Topics ( with M. Grabchak, V. Panov) in the Notes of the Research Seminars of the St. Petersburg Institute of Mathematics 2022, Vol.515, pp 91-120.

##### XI. New Topics

- “Quasicumulants and limit theorems in case of the Cauchy limiting law”, Markov Processes Related Fields, 13 (2007), 597-624 (with V.V. Petrov and N. Squartini).
- “On bounded solutions of the balanced generalized pantograph equation”. In “Topics in Stochastic Analysis and Nonparametric Estimation”, IMA Vol.Math.Appl., 145, 29-49, Springer, NY, 2008.
- “On measuring nonlinear risk with scarce observation”, Finance Stoch., published on line Nov.2009, D)I 10.00780-009-0707-y
- “Explicit parametrix and local limit theorems doe the degenerated Markov processes”, Ann. I Inst. Henry Poincare, 2010, 46(4), pp. 908 ” 923 (with V. Konakov, S. Menozzi). “A solvable model for homopolymers and self-similarity near the critical point”, Rand. Operators and Stochastic Equations (ROSE), 2010, 18 (1), pp.73-95 (with M. Cranston, L. Koralov and B. Vainberg)
- “Two Markov models of the spread of the rumors “, Journ. Math Sociology, 2010, 34(3), pp. 157-166 (with J. Whitmeyer)
- “Wave propagation in periodic network of thin fibers”, Integral methods in Sci. and Engineering, Vol.I, Birkhauser Verlag, 2010, pp.255-278 (with B. Vainberg).
- “Diffusion processes on solvable groups of upper triangular (2 2) matrices and their Approximation”, Doklady Acad. Nauk (Russian Academy of Sci.), 2011, Vol.439,#4, pp.585-588 (with. V. Konakov and S. Menozzi).
- “Negative spectra of elliptic operators” (with O. Safronov), Bull. Math.Sci., D -1-10-1007 S, 11373-012-0025-8, 9 pp.
- “On the decoupling of functions of Normal vectors” (with P.Grigoriev), II Mat. Zametki, 94 #2, 310 313
- “Large deviation for the symmetric branching random walk on multi-dimensional lattice” (with E. Yarovaya), Trudy Steklov Inst. Of Math., RAN, vol.282, 1 16 (in Russian and English)
- ” Structure of the population inside the propagating front” (with L. Koralov), J. Math. Sci., Vol.189, #4, 637 659
- “Limit theorems and phase transitions for i.i.d.r.v. depending on parameters” (with M. Grabchak), Doklady Russ.Acad.Sci. , Vol.88, 31, 431-434
- A mean field approximation of the Bolker – Pacala population model (with M. Bessonov and J. Whitmeyer), 2014, 20:329 – 348
- Density behavior of spatial birth – and -death stochastic evolution of mutating genotypes under selection rates (with D. Finkelshtein, Yu. Kondratiev, O. Kutoviy, E. Zhizhina) in Russian Journal on Math. Phys., 21:4(2014), pp. 61 – 98
- Summation of independent rave. with heavy tails: phase transition and limit theorems, in Probab. Theory and Appl. (with M. Grabchak)
- Limit Theorems and Phase Transitions for Two Models of Summation of iid Random Variables with a Parameter (with M. Grabchak), Teoriya Veroyatnostei i ee Primeneniya, 2014, 59(2): 340 – 364
- S. Molchanov (with L. Pastur and E. Ray). Examples of Random Schrodinger-typeOperators with Non-Poissonian Spectra. In Markov Processes and Related Fields. 2015, V. 21, # 3, pp. 713 749
- S. Molchanov (with A. Getaan and B. Vainberg), Intermittency for branching walk with heavy tails, in Stochastic and Dynamics, 2016, Vol.17, #6, (14 pp)

##### XII. Courses Authored

- “Introduction to the Spectral Theory”, 2013
- “Spectral theory on the fractals”, 2012
- “Spectral theory of 1D Schroedinger operators”, 2011
- “Topics in mathematics (Introduction to fractals)”, 2011
- Mini-course “Quenched and annealed asymptotics in random media theory”, 6 lectures, University of Paris-7 (Paris, France), June 2010
- Mini-course “Mathematical models in population dynamics”, 6 lectures, University of Bielefeld (Bielefeld, Germany), July 2010
- Mini-course “Qualitative spectral analysis”, 8 lectures, Moscow University, December 2010.
- Multi-level course “Applied Probability”. The course will have four levels:

a. Applied probability I (basic models and limit theorems)

b. Applied probability II (Markov chains, renewal theory, queuing theory)

c. Applied probability III (Time series ; forecast, interpolation, spectral analysis) - Seminar in Real Analysis ( fall 2007 – spring 2008)
- “Introduction to the differential geometry” (Math 4080, Math5080) (Spring 2006)
- New Ph.D. level course “Introduction to the theory of quantum graphs” was developed for University of California (Irvine). The lecture notes are in the preparation for publication. This course will be repeated at UNCC.(Fall 2006)
- “Asymptotic methods in the analysis”, (Math 7050, Math 8050) (Spring 2005)
- “Spectral theory of the Schrdinger operators on the general graphs ” (4 lectures), Bielefeld, Germany, June 2014
- “Spectral theory of the convolution type operators with applications to the population dynamics” (4 lectures), Bielefeld, Germany, July 2014
- Special Course “Introduction to the Spectral Theory,” UNCC, Fall 2018.
- Developed and gave a mini-course (3 lectures) at the conference “Perturbation techniques in stochastic analysis and its applications: perturbation problems in the population dynamics,” CIRM, Marseille, France, March 2019.
- Mini-course “Introduction to risk theoy,” National Research University “Higher School of Economics”, Moscow, Russia, December 2019.
- Mini-course at Isaac Newton Institute for Mathematical Sciences at Cambridge University, Cambridge, UK, April 2022. Curriculum of this mini-course: 1. Fractal lattices. The Sierpinski lattice as a typical example. Random walk on these lattices. 2. Spectral theory on the abovementioned lattices. Spectral dimension. 3. Schrödinger operator on the Sierpinski lattice with random potential (Anderson model). Cluster expansion on the resolvent. Localization theorem. 4. Hierarchical models.Dyson lattice and the spectrum of the corresponding Laplacian. 5. Continuous hierarchical models. Localization theorem for the class of the random potentials of the finite rank. 6. Airy hierarchical model and its random perturbations.
- Mini-course at the the University Paris Sergy, France, Neuville-sur Oise. July 5 – July 8. 2022. “On the ensemble concept in probability theory and mathematical physics”, 4 lectures. The lecture notes will be published.
- New Ph.D. course “The Introduction to Differential and Riemannian geometry”, Fall 2022 5 students attended this class, including my own Ph.D. students Madhumita Paul and Wai-lun Lam.

Wai-lun’ thesis will be based on the theory of the diffusion processes and Markov chain on the compact Riemannian manifolds. 2. Seminar “Arnold’ Problems” (Math 8050) for the graduate and undergraduate students (with Dr. Yu. Godin).