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Papers by Mark Freidlin

Research paper thumbnail of On diffusions in media with pockets of large diffusivity

arXiv (Cornell University), Oct 10, 2017

Research paper thumbnail of Asymptotics in the Dirichlet Problem for Second Order Elliptic Equations with Degeneration on the Boundary

arXiv (Cornell University), Jun 29, 2021

Research paper thumbnail of Averaging in the case of multiple invariant measures for the fast system

arXiv (Cornell University), Feb 23, 2020

Research paper thumbnail of Perturbations of Parabolic Equations and Diffusion Processes with Degeneration: Boundary Problems, Metastability, and Homogenization

arXiv (Cornell University), Dec 28, 2021

Research paper thumbnail of On the motion of light particles perturbed by noise

Russian Mathematical Surveys, 2000

Research paper thumbnail of Asymptotics in the Dirichlet problem for second order elliptic equations with degeneration on the boundary

Journal of Differential Equations

Research paper thumbnail of Averaging in the case of multiple invariant measures for the fast system

Electronic Journal of Probability, 2021

We consider the averaging principle for deterministic or stochastic systems with a fast stochasti... more We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in the simplex of invariant probability measures of the chains, the limiting system should be considered on a graph or on an open book with certain gluing conditions in the vertices of the graph (or on the bifurcation surface).

Research paper thumbnail of Fast flow asymptotics for stochastic incompressible viscous fluids in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math></span><span class="katex-html" aria-hidden="true"></span></span>\mathbb {R}^2$$R2 and SPDEs on graphs

Probability Theory and Related Fields, 2018

Research paper thumbnail of On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior

Discrete & Continuous Dynamical Systems - A, 2016

Research paper thumbnail of Surveys in Applied Mathematics

Research paper thumbnail of Perturbation of Systems with a First Integral: Motion on the Reeb Graph

Journal of Statistical Physics

Research paper thumbnail of On diffusions in media with pockets of large diffusivity

Probability Theory and Related Fields, 2019

Research paper thumbnail of Surveys in Applied Mathematics. Vol. 2

Research paper thumbnail of AVERAGING PRINCIPLE FOR QUASI-LINEAR PARABOLIC PDEs AND RELATED DIFFUSION PROCESSES

Stochastics and Dynamics, 2012

Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding ... more Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDEs with a small parameter at the second-order derivatives are considered in this paper.

Research paper thumbnail of Wave front propagation for a reaction–diffusion equation in narrow random channels

Research paper thumbnail of On Perturbations of Generalized Landau-Lifshitz Dynamics

Journal of Statistical Physics, 2011

Research paper thumbnail of On Diffusion in Narrow Random Channels

Journal of Statistical Physics, 2013

Research paper thumbnail of Smoluchowski–Kramers approximation in the case of variable friction

Journal of Mathematical Sciences, 2011

Research paper thumbnail of Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus

Ergodic Theory and Dynamical Systems, 2012

We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional ... more We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such flows can be stochastic. The stochasticity is caused by instabilities near the saddle points as well as by the ergodic component of the locally Hamiltonian system on the torus.

Research paper thumbnail of On Second Order Elliptic Equations with a Small Parameter

Communications in Partial Differential Equations, 2013

Research paper thumbnail of On diffusions in media with pockets of large diffusivity

arXiv (Cornell University), Oct 10, 2017

Research paper thumbnail of Asymptotics in the Dirichlet Problem for Second Order Elliptic Equations with Degeneration on the Boundary

arXiv (Cornell University), Jun 29, 2021

Research paper thumbnail of Averaging in the case of multiple invariant measures for the fast system

arXiv (Cornell University), Feb 23, 2020

Research paper thumbnail of Perturbations of Parabolic Equations and Diffusion Processes with Degeneration: Boundary Problems, Metastability, and Homogenization

arXiv (Cornell University), Dec 28, 2021

Research paper thumbnail of On the motion of light particles perturbed by noise

Russian Mathematical Surveys, 2000

Research paper thumbnail of Asymptotics in the Dirichlet problem for second order elliptic equations with degeneration on the boundary

Journal of Differential Equations

Research paper thumbnail of Averaging in the case of multiple invariant measures for the fast system

Electronic Journal of Probability, 2021

We consider the averaging principle for deterministic or stochastic systems with a fast stochasti... more We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in the simplex of invariant probability measures of the chains, the limiting system should be considered on a graph or on an open book with certain gluing conditions in the vertices of the graph (or on the bifurcation surface).

Research paper thumbnail of Fast flow asymptotics for stochastic incompressible viscous fluids in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math></span><span class="katex-html" aria-hidden="true"></span></span>\mathbb {R}^2$$R2 and SPDEs on graphs

Probability Theory and Related Fields, 2018

Research paper thumbnail of On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior

Discrete & Continuous Dynamical Systems - A, 2016

Research paper thumbnail of Surveys in Applied Mathematics

Research paper thumbnail of Perturbation of Systems with a First Integral: Motion on the Reeb Graph

Journal of Statistical Physics

Research paper thumbnail of On diffusions in media with pockets of large diffusivity

Probability Theory and Related Fields, 2019

Research paper thumbnail of Surveys in Applied Mathematics. Vol. 2

Research paper thumbnail of AVERAGING PRINCIPLE FOR QUASI-LINEAR PARABOLIC PDEs AND RELATED DIFFUSION PROCESSES

Stochastics and Dynamics, 2012

Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding ... more Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDEs with a small parameter at the second-order derivatives are considered in this paper.

Research paper thumbnail of Wave front propagation for a reaction–diffusion equation in narrow random channels

Research paper thumbnail of On Perturbations of Generalized Landau-Lifshitz Dynamics

Journal of Statistical Physics, 2011

Research paper thumbnail of On Diffusion in Narrow Random Channels

Journal of Statistical Physics, 2013

Research paper thumbnail of Smoluchowski–Kramers approximation in the case of variable friction

Journal of Mathematical Sciences, 2011

Research paper thumbnail of Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus

Ergodic Theory and Dynamical Systems, 2012

We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional ... more We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such flows can be stochastic. The stochasticity is caused by instabilities near the saddle points as well as by the ergodic component of the locally Hamiltonian system on the torus.

Research paper thumbnail of On Second Order Elliptic Equations with a Small Parameter

Communications in Partial Differential Equations, 2013

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