Fluctuation-dissipation relations for reversible diffusions in a random environment

“Fluctuation-dissipation relations” The lecture will be devoted to a soft introduction to FDR for additive functionals of Markov processes. Pierre MATHIEU

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 of 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.