Fluctuation-dissipation 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
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.
-
- “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
-
- “Fluctuation-dissipation 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
Related Courses
![](https://ocw.kyoto-u.ac.jp/en/wp-content/uploads/sites/2/2022/05/3294_top-1568x882.jpg)
Masae Ishihara, Yasuyuki Shibata
Graduate School of Science, Field Science Education and Research Center
2021![](https://ocw.kyoto-u.ac.jp/en/wp-content/uploads/sites/2/2022/01/20211108spectrum_of_random_graphs.jpg)
Prof. Charles Bordenave
Graduate School of Science
2021![](https://ocw.kyoto-u.ac.jp/en/wp-content/uploads/sites/2/2021/10/SuperGlobal_L4_Tn.jpg)
Stephen Theriault
Graduate School of Science
2021![](https://ocw.kyoto-u.ac.jp/en/wp-content/uploads/sites/2/2019/07/2019_Vertex-algebras-instanton-counting-and-invariants-of-3-and-4-dimensional-manifolds.jpg)
Boris FEIGIN
Graduate School of Science
2019