Fluctuation-dissipation relations for reversible diffusions in a random environment

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

講義詳細

年度・期
2017年度・後期集中
開催日
2017年11月10日 から 12月01日
開講部局名
理学研究科
使用言語
英語
教員/講師名
Pierre MATHIEU(Distinguished Visiting Professor, Kyoto University)
開催場所
Room 127, Graduate School of Science Bldg No 3
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