Open Access
2017 Metastability in the reversible inclusion process
Alessandra Bianchi, Sander Dommers, Cristian Giardinà
Electron. J. Probab. 22: 1-34 (2017). DOI: 10.1214/17-EJP98


We study the condensation regime of the finite reversible inclusion process, i.e., the inclusion process on a finite graph $S$ with an underlying random walk that admits a reversible measure. We assume that the random walk kernel is irreducible and its reversible measure takes maximum value on a subset of vertices $S_{\star }\subseteq S$. We consider initial conditions corresponding to a single condensate that is localized on one of those vertices and study the metastable (or tunneling) dynamics. We find that, if the random walk restricted to $S_{\star }$ is irreducible, then there exists a single time-scale for the condensate motion. In this case we compute this typical time-scale and characterize the law of the (properly rescaled) limiting process. If the restriction of the random walk to $S_{\star }$ has several connected components, a metastability scenario with multiple time-scales emerges. We prove such a scenario, involving two additional time-scales, in a one-dimensional setting with two metastable states and nearest-neighbor jumps.


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Alessandra Bianchi. Sander Dommers. Cristian Giardinà. "Metastability in the reversible inclusion process." Electron. J. Probab. 22 1 - 34, 2017.


Received: 11 February 2017; Accepted: 21 August 2017; Published: 2017
First available in Project Euclid: 13 September 2017

zbMATH: 06797880
MathSciNet: MR3698739
Digital Object Identifier: 10.1214/17-EJP98

Primary: 60K35 , 82C20 , 82C22

Keywords: capacity , inclusion process , metastability , potential theory

Vol.22 • 2017
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