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Teoriya Veroyatnostei i ee Primeneniya, 2021, Volume 66, Issue 2, Pages 231–260
DOI: https://doi.org/10.4213/tvp5467 (Mi tvp5467) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Breaking a chain of interacting Brownian particles: a Gumbel limit theorem

F. Aurzadaa, V. Betza, M. A. Lifshitsb

a Technische Universität Darmstadt, Darmstadt
b Saint-Petersburg State University, Department of Mathematics and Computer Science
Full-text PDF (534 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp5467
Abstract: We investigate the behavior 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. In the regime where both the pulling and the noise significantly influence the behavior of the chain, we prove weak limit theorems for the break time and the break position.
Keywords: interacting Brownian particles, stochastic differential equations, Ornstein–Uhlenbeck processes.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-12004
Deutsche Forschungsgemeinschaft AU370/7
This work was supported by the Russian Foundation for Basic Research (grant 20-51-12004) and Deutsche Forschungsgemeinschaft (grant AU370/7).
Received: 20.12.2020
English version:
Theory of Probability and its Applications, 2021, Volume 66, Issue 2, Pages 184–208
DOI: https://doi.org/10.1137/S0040585X97T990344
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: F. Aurzada, V. Betz, M. A. Lifshits, “Breaking a chain of interacting Brownian particles: a Gumbel limit theorem”, Teor. Veroyatnost. i Primenen., 66:2 (2021), 231–260; Theory Probab. Appl., 66:2 (2021), 184–208
Citation in format AMSBIB
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  • https://doi.org/10.4213/tvp5467
  • https://www.mathnet.ru/eng/tvp/v66/i2/p231
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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