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2018 Metastability of hard-core dynamics on bipartite graphs
Frank den Hollander, Francesca R. Nardi, Siamak Taati
Electron. J. Probab. 23: 1-65 (2018). DOI: 10.1214/18-EJP210

Abstract

We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion constraint, while existing particles disappear, all according to independent Poisson clocks. We consider the regime in which the appearance rates are much larger than the disappearance rates, and there is a slight imbalance between the appearance rates on the two parts of the graph. Starting from the configuration in which the weak part is covered with particles, the system takes a long time before it reaches the configuration in which the strong part is covered with particles. We obtain a sharp asymptotic estimate for the expected transition time, show that the transition time is asymptotically exponentially distributed, and identify the size and shape of the critical droplet representing the bottleneck for the crossover. For various types of bipartite graphs the computations are made explicit. Proofs rely on potential theory for reversible Markov chains, and on isoperimetric results.

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Frank den Hollander. Francesca R. Nardi. Siamak Taati. "Metastability of hard-core dynamics on bipartite graphs." Electron. J. Probab. 23 1 - 65, 2018. https://doi.org/10.1214/18-EJP210

Information

Received: 12 January 2018; Accepted: 8 August 2018; Published: 2018
First available in Project Euclid: 21 September 2018

zbMATH: 06964791
MathSciNet: MR3862612
Digital Object Identifier: 10.1214/18-EJP210

Subjects:
Primary: 60C05 , 60K35 , 60K37 , 82C27

Keywords: bipartite graphs , interacting particle systems , isoperimetric problems , metastability , potential theory

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