Breaking a chain of interacting Brownian particles
Probability
2019-12-12 v1
Abstract
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small Brownian noise. We study the instant when the chain "breaks", that is, the distance between two neighboring particles becomes larger than a certain limit. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise. We prove weak limit theorems for the break time and the break position for each regime.
Keywords
Cite
@article{arxiv.1912.05168,
title = {Breaking a chain of interacting Brownian particles},
author = {Frank Aurzada and Volker Betz and Mikhail Lifshits},
journal= {arXiv preprint arXiv:1912.05168},
year = {2019}
}
Comments
60 pages