23 - Fluctuation-dissipation relations for reversible diffusions in a random environment, 2017

Top Glogal Course Special Lectures 6 Fluctuation-dissipation relations for reversible diffusions in a random environment Pierre Mathieu Kyoto University / Distinguished Visiting Professor Aix-Marseille université / Professor Nov. 10, 17, 24, 29 and Dec. 1, 2017 Room127, Graduate School of Science Bldg No 3 Lecture Video

Course Description

Fluctuation-dissipation relations (FDR) were introduced in statistical physics to describe off-equilibrium dynamics; they express the linear response of a perturbed system as correlations for the un-perturbed system.

When applied to reversible diffusions in a random environment, they yield the so-called Einstein relation: the derivative of the effective drift of a diffusion in a random environment subject to a small external force equals the effective variance of the un-perturbed dynamics in the direction of the perturbation.

The aim the course will be to explain the proof of FDR for reversible diffusions in a random environment with finite range of correlation. The proof also provides a full description of all the scaling limits of such processes.