Kyoto U. 'Fluctuation-dissipation relations for reversible diffusions in a random environment' L.5

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"Fluctuation-dissipation relations for reversible diffusions in a random environment"
Lecture 5

Pierre Mathieu
Kyoto University / Distinguished Visiting Professor
Aix-Marseille université / Professor

Nov. 10, 17, 24, 29 and Dec. 1, 2017
Room 127, Graduate School of Science Bldg No 3

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.

Lecture 5
"FDR and scaling limits" End of the proof of FDR and the Einstein relation.

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