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Metastability in the reversible inclusion process

Bianchi, Alessandra; Dommers, Sander; Giardinà, Cristian

Authors

Alessandra Bianchi

Dr Sander Dommers S.Dommers@hull.ac.uk
Lecturer in Statistics, Director of Studies Mathematics

Cristian Giardinà



Abstract

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.

Journal Article Type Article
Publication Date Sep 13, 2017
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
APA6 Citation Bianchi, A., Dommers, S., & Giardinà, C. (2017). Metastability in the reversible inclusion process. Electronic journal of probability, 22, doi:10.1214/17-EJP98
DOI https://doi.org/10.1214/17-EJP98
Publisher URL https://projecteuclid.org/euclid.ejp/1505268101#abstract
Copyright Statement Creative Commons Attribution 4.0 International License.

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Copyright Statement
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