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

Fluctuation-dissipation relations for reversible diffusions in a random environment

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.