TU Berlin

Sonderforschungsbereich 910Quantitative estimates in stochastic homogenization

SFB logo

Inhalt

zur Navigation

Es gibt keine deutsche Übersetzung dieser Webseite.

Quantitative estimates in stochastic homogenization

Abstract:

We consider the (steady-state) diffusion equation on the integer lattice with random coefficients. For stationary and ergodic coefficients a homogenized behavior emerges on large length scales; that is, in the macroscopic limit the random coefficient field can be effectively replaced by homogenized coefficients that are deterministic and constant in space. This is a great reduction of complexity!

The homogenized coefficients are defined via a formula that involves the solution to the so called "corrector problem". In contrast to periodic homogenization, in the stochastic setting the corrector problem is posed on an infinite-dimensional function space; and thus, its analysis becomes ricky.

In this talk we present quantitative estimates on the corrector equation. They rely on the observation that ergodicity can be quantified by combining a certain spectral gap property and estimates on the parabolic Green’s function.

This is joint work with Antoine Gloria, INRIA Lille, and Felix Otto, MPI Leipzig.

Navigation

Direktzugang

Schnellnavigation zur Seite über Nummerneingabe