A Probabilistic view on the homogenization of the heat equation

  • Jean-Christophe Mourrat (École polytechnique fédérale de Lausanne)
A3 01 (Sophus-Lie room)


Consider the heat equation with random coefficients on Z^d. The randomness of the coefficients models the inhomogeneous nature of the medium where heat propagates. We assume that the distribution of these coefficients is invariant under spatial translations, and has a finite range of dependence. It is known that if a solution to this equation is rescaled diffusively, then it converges to the solution of a heat equation with constant coefficients. I will first explain how this convergence can be rephrased in terms of the long-time behaviour of an associated random walk. Based on this representation, I will then present recent progress on the estimation of the speed of this convergence.

26.11.96 27.06.24

Oberseminar Analysis

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E2 10 (Leon-Lichtenstein) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Augusteum - A314

Anne Dornfeld

MPI for Mathematics in the Sciences Contact via Mail