Evolution of a passive particle in a one-dimensional diffusive environment

被引：0

作者：

Huveneers, Francois ^{[1
]}

Simenhaus, Francois ^{[1
]}

机构：

[1] Univ Paris 09, Ceremade, Paris, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2023年 / 28卷

关键词：

random walks in dynamical random environment; limit theorems; scaling limits; DYNAMIC RANDOM-ENVIRONMENTS; RANDOM-WALK; SYMMETRIC EXCLUSION;

D O I：

10.1214/22-EJP896

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time limit, we show that the fluctuations of the particle become Gaussian and sub-diffusive, with dynamical exponent 3/4. Second, in the long time limit, we show that the particle is trapped by the local minima of the potential and evolves diffusively i.e. with exponent 1/2.

引用

页数：32

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