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Metastability in the reversible inclusion process

Bianchi, Alessandra; Dommers, Sander; Giardinà, Cristian


Alessandra Bianchi

Sander Dommers

Cristian Giardinà


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⋆⊆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⋆ 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⋆ 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.


Bianchi, A., Dommers, S., & Giardinà, C. (2017). Metastability in the reversible inclusion process. Electronic journal of probability, 22, Article 70.

Journal Article Type Article
Acceptance Date Aug 21, 2017
Online Publication Date Sep 13, 2017
Publication Date Sep 13, 2017
Deposit Date Jun 28, 2018
Publicly Available Date Jul 12, 2018
Journal Electronic Journal of Probability
Print ISSN 1083-6489
Electronic ISSN 1083-6489
Publisher Institute of Mathematical Statistics (IMS)
Peer Reviewed Peer Reviewed
Volume 22
Article Number 70
Public URL
Publisher URL


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