Geodesic
Breaking a~chain of interacting Brownian particles: a~Gumbel limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 231-260

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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. 
@article{TVP_2021_66_2_a1,
     author = {F. Aurzada and V. Betz and M. A. Lifshits},
     title = {Breaking a~chain of interacting {Brownian} particles: {a~Gumbel} limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {231--260},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a1/}
}
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F. Aurzada; V. Betz; M. A. Lifshits. Breaking a~chain of interacting Brownian particles: a~Gumbel limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 231-260. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a1/