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Metastability in the reversible inclusion process

Bianchi, Alessandra; Dommers, Sander; Giardinà, Cristian


Alessandra Bianchi

Dr Sander Dommers
Lecturer in Statistics, Director of Studies Mathematics

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.

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
Publisher URL
Copyright Statement Creative Commons Attribution 4.0 International License.


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Copyright Statement
Creative Commons Attribution 4.0 International License.

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