Quantitative Einstein relation for reversible diffusions in a random environment

Fuente: arXiv
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Main Authors: Bou-Rabee, Ahmed, Xu, Ruizhe
Format: Preprint
Published: 2026
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author Bou-Rabee, Ahmed
Xu, Ruizhe
author_facet Bou-Rabee, Ahmed
Xu, Ruizhe
contents The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity matrix of the unforced particle, evaluated in the force direction. Gantert, Mathieu, and Piatnitski (2012) proved this identity for reversible diffusions in random environments. We prove a quantitative version, with an explicit quenched algebraic rate.
format Preprint
id arxiv_https___arxiv_org_abs_2605_26082
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Quantitative Einstein relation for reversible diffusions in a random environment
Bou-Rabee, Ahmed
Xu, Ruizhe
Probability
Analysis of PDEs
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity matrix of the unforced particle, evaluated in the force direction. Gantert, Mathieu, and Piatnitski (2012) proved this identity for reversible diffusions in random environments. We prove a quantitative version, with an explicit quenched algebraic rate.
title Quantitative Einstein relation for reversible diffusions in a random environment
topic Probability
Analysis of PDEs
url https://arxiv.org/abs/2605.26082