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December 2021 Breaking a chain of interacting Brownian particles
Frank Aurzada, Volker Betz, Mikhail Lifshits
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Ann. Appl. Probab. 31(6): 2585-2611 (December 2021). DOI: 10.1214/20-AAP1658

Abstract

We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise linear force, 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 neighbouring particles becomes larger than a certain threshold. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise. We provide weak limit theorems for the break time and the break position for each regime.

Funding Statement

The first and third authors were supported by the co-ordinated grants of DFG (GO420/6-1) and RFBR (no. 20-51-12004).

Acknowledgement

We would like to thank the anonymous referees and the Associate Editor for carefully reviewing our manuscript and for their questions that inspired the results in Section 3.3.

We are also grateful to Dr. N. Gorn for encouraging computer simulations.

Citation

Download Citation

Frank Aurzada. Volker Betz. Mikhail Lifshits. "Breaking a chain of interacting Brownian particles." Ann. Appl. Probab. 31 (6) 2585 - 2611, December 2021. https://doi.org/10.1214/20-AAP1658

Information

Received: 1 December 2019; Revised: 1 June 2020; Published: December 2021
First available in Project Euclid: 13 December 2021

Digital Object Identifier: 10.1214/20-AAP1658

Subjects:
Primary: 60K35
Secondary: 60G15 , 60H10 , 60J70

Keywords: Interacting Brownian particles , Ornstein–Uhlenbeck processes , Stochastic differential equation

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 6 • December 2021
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