List of publications
M.
Freidlin, L. Koralov, Perturbations of Parabolic
Equations and Diffusion Processes with Degeneration: Boundary Problems,
Metastability, and Homogenization, submitted to Journal of American
Mathematical Society.
M.
Freidlin, L. Koralov, Asymptotics
in the Dirichlet Problem for Second Order Elliptic Equations with Degeneration
on the Boundary, submitted to Journal of Differential Equations.
L.
Koralov, B. Vainberg, Global Limit Theorem for
Parabolic Equations with a Potential, to appear in SIAM Journal on Mathematical
Analysis.
L.
Koralov, S. Molchanov, B. Vainberg,
On the Near-Critical Behavior of Continuous Polymers, to appear in Pure and
Applied Functional Analysis.
L.
Koralov, S. Molchanov, B. Vainberg,
The Radius of a Polymer at a Near-Critical Temperature, to appear in Applicable
Analysis.
M.
Freidlin, L. Koralov, Averaging in the case of
multiple invariant measures for the fast system, Electronic Journal of
Probability 26 (2021), Paper No 138, 17 pp.
P.
Hebbar, L. Koralov, J. Nolen, Asymptotic behavior of branching
diffusion processes in periodic media. Electronic Journal of Probability,
25 (2020), Paper No 126, 40 pp.
M.
Freidlin, L. Koralov, Diffusion in the presence of
cells with semi-permeable membranes, Journal of Statistical Physics, 178
(2020), no 6, pp 1417-1441.
M.
Freidlin, L. Koralov, A. Wentzell.
On diffusion in media with pockets of large diffusivity, Probability Theory and
Related Fields, 175(1) (2019), pp 559-578.
M. Freidlin, L.
Koralov. Front propagation for reaction-diffusion
equations in composite structures. Journal of Statistical
Physics, 172 (2018), no. 6, 1663--1681.
D. Dolgopyat, P. Hebbar, L. Koralov, M. Perlman. Multi-type branching processes with
time-dependent branching
rates. Journal of Applied Probability 55 (2018), no. 3, 701--727.
M. Hairer, G. Iyer,
L. Koralov, A. Novikov, Z. Pajor-Gyulai. A fractional kinetic process
describing the intermediate time behavior of cellular flows. Annals
of Probability, 46 (2018), no. 2, pp 897--955.
M. Freidlin, L. Koralov. Metastable distributions of
Markov chains with rare transitions. Journal of Statistical
Physics., 167 (2017), no 6, pp 1355--1375.
M. Freidlin, L. Koralov. On stochastic perturbations
of slowly changing dynamical systems. Nonlinearity, 30 (2017), no
1, pp 445--453.
M. Freidlin, L. Koralov, A. Wentzell.
On the
behavior of diffusion processes with traps.
Annals of Probability. 45 (2017),
no 5, pp. 3203--3222.
M. Hairer, L. Koralov, Z. Pajor-Gyulai.
From averaging to homogenization in cellular
flows – an exact description of the transition.
Annales de l’Institut Henri Poincare – Probabilites et
Statistiques, (2016), Vol 52, No4, pp 1592-1612.
L. Koralov,
L. Tcheuko. Quasi-linear
equations with a small diffusion term and the evolution of hierarchies of
cycles. Journal
of Theoretical Probability, (2016), Vol 29, pp 867-895.
L.
Koralov, S. Molchanov, B. Vainberg.
On mathematical foundation of Brownian motor
theory (diffusion in periodic channels). Journal of Functional
Analysis, 267 (2014), no 6, pp 1725-1750.
L.
Koralov, Z. Pajor-Gyulai. On the critical behavior of continuous
homopolymers. Stochastics and
Dynamics, (2014), Vol 14, No 1.
L.
Koralov, S. Molchanov. Branching diffusion processes
and intermittency, preprint.
L. Koralov,
S. Molchanov. The structure of the
population inside the propagating front. Journal of Mathematical
Sciences (Problems in Mathematical Analysis) (2013), Vol 189, no 4, pp 637-658.
D. Dolgopyat, L. Koralov. Averaging
of incompressible flows on two-dimensional surfaces. Journal
of American Mathematical Society (2013), Vol 26, no 2, pp 427-449.
L. Koralov.
Branching diffusion in
inhomogeneous media. Asymptotic Analysis, (2013), Vol 81,
no 3-4, pp 357-377.
M.
Freidlin, L. Koralov. Averaging Principle for quasi-linear
parabolic PDE's and related diffusion processes. Stochastics and
Dynamics, (2012), Vol 12, No 1.
D.
Dolgopyat, M. Freidlin, L.
Koralov. Deterministic
and Stochastic Perturbations of Hamiltonian Systems on a 2-dimensional torus. Ergodic Theory and Dynamical Systems
(2012), Vol 32, issue 3, pp 899-918.
M.
Freidlin, L. Koralov. Metastability for Nonlinear Random
Perturbations of Dynamical Systems, Stochastic Processes and
Applications 120 (2010), no. 7, 1194–1214.
M.
Freidlin, L. Koralov. Nonlinear Stochastic Perturbations of Dynamical
Systems, Probability Theory and Related Fields (2010), 147, pp 273-301.
M.
Cranston, L. Koralov, S. Molchanov, B. Vainberg. A
Solvable Model for Homopolymers and Critical Phenomena. Random
Operators and Stochastic Equations 18 (2010), no. 1, 73–95.
M.
Cranston, L. Koralov, S. Molchanov, B. Vainberg. Continuous
Model for Homopolymers, Jounal of Functional
Analysis 256 (2009), no 8, pp 2656-2696.
D.
Dolgopyat, L. Koralov. Motion in Random Force Field,
Nonlinearity, 22 (2009), pp 187-211.
L.
Koralov. An Inverse Problem
for Gibbs Fields with Hard Core Potential, Journal of Mathematical
Physics, 48, No 5, 2007.
L.
Koralov. An Inverse Problem for Gibbs Fields, CRM Proceedings and
Lecture Notes, 2007.
D.
Dolgopyat, L. Koralov. Averaging of Hamiltonian Flows with an
Ergodic Component, Annals of Probability, 36 (2008), pp 1999-2049.
L.
Koralov. The Existence of Pair Potential
Corresponding to Specified Density and Pair Correlation, Letters in
Mathematical Physics (2005), 71, pp 135-148.
L.
Koralov, Ya. Sinai. Probability Theory, Random
Processes and Random Fields,
Textbook, Springer-Verlag, 2007.
D.
Dolgopyat, V. Kaloshin, L.
Koralov. Long time behavior of periodic stochastic dispersion, XIVth International Congress on Mathematical Physics, 290--295, World Sci. Publ., Hackensack, NJ,
2005.
L.
Koralov. Random
Perturbations of 2-Dimensional Hamiltonian Flows, Probability Theory
and Related Fields 129, pp 37-62, 2004.
D.
Dolgopyat, V. Kaloshin, L.
Koralov. Sample Path Properties of the Stochastic Flows, Annals of
Probability, 32 no 1A, pp 1-27, 2004.
D.
Dolgopyat, V. Kaloshin, L.
Koralov. A Limit
Shape Theorem for Periodic Stochastic Dispersion, Communications in
Pure and Applied Mathematics, 57 (2004), no 9, pp 1127-1158.
D.
Dolgopyat, V. Kaloshin, L.
Koralov. Hausdorff Dimension in Stochastic
Dispersion, Journal of Statistical Physics, Vol 108, Nos 5/6, pp 943-972
(2002).
R. Carmona, L.
Koralov, S. Molchanov. Asymptotics
for the Almost Sure Lyapunov Exponent for the Solution of the Parabolic
Anderson Problem,
Random Operators and Stochastic Equations, Vol 9, No. 1, pp 77-86
(2001).
L.
Koralov. Transport by Vector Fields with
Kolmogorov Spectrum, Journal of Statistical Physics, Vol 98, Issue 1/2, pp
405-418 (2000)
L.
Koralov. Transport by
Time Dependent Stationary Random Flow, Communications in Mathematical
Physics, 199, pp 649-681 (1999)
L.
Koralov. Effective Diffusivity of Stationary Vector Fields with Short Time
Correlations, Random Operators and Stochastic Equations, no 4, Vol
5, pp 303-324 (1997).
L. Koralov, S. Nechaev, Ya. Sinai.
Limit Behavior of a two-dimensional Random Walk with Topological Constraints,
Theory Probab. Appl 38 (1993), no 2, 296-306.
L.
Koralov, S. Nechaev, Ya. Sinai.
Limiting Probability Distribution for a Random Walk with Topological
Constraints, Chaos 1 (1991), no 2, 131-133.