Fluctuationdissipation relations for reversible diffusions in a random environment
“Central limit theorems” We shall first survey the martingale approach to establish the convergence towards Brownian motion of a reversible diffusion in a random environment. Pierre MATHIEU
Course Description
Fluctuationdissipation relations (FDR) were introduced in statistical physics to describe offequilibrium dynamics; they express the linear response of a perturbed system as correlations for the unperturbed system.
When applied to reversible diffusions in a random environment, they yield the socalled 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 unperturbed 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.

 “Central limit theorems” We shall first survey the martingale approach to establish the convergence towards Brownian motion of a reversible diffusion in a random environment.

Pierre MATHIEU
Dec. 01, 2017 1:52:48 English

 “Fluctuationdissipation relations” The lecture will be devoted to a soft introduction to FDR for additive functionals of Markov processes.

Pierre MATHIEU
Dec. 01, 2017 1:54:10 English

 “A priori estimates on diffusions” We gather some PDE estimates for diffusions with a local drift.

Pierre MATHIEU
Dec. 01, 2017 1:52:33 English

 “Regeneration times and steady states” We construct a steady state for perturbed diffusions in a random environment with finite range of correlation and study its continuity.

Pierre MATHIEU
Dec. 01, 2017 2:03:38 English

 “FDR and scaling limits” End of the proof of FDR and the Einstein relation.

Pierre MATHIEU
Dec. 01, 2017 1:55:53 English
Details
 Year/Term
 2017 / Intensive, Second semester
 Date
 November 10th to December 1st, 2017
 Faculty/
Graduate School  Graduate School of Science
 Language
 English
 Instructor name
 Pierre MATHIEU（Distinguished Visiting Professor, Kyoto University）
 Place
 Room 127, Graduate School of Science Bldg No 3
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