Metastability in the reversible inclusion process

Bianchi, Alessandra; Dommers, Sander; Giardinà, Cristian

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.

Citation

Bianchi, A., Dommers, S., & Giardinà, C. (2017). Metastability in the reversible inclusion process. Electronic journal of probability, 22, Article 70. https://doi.org/10.1214/17-EJP98

• 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
• Publisher: Institute of Mathematical Statistics (IMS)
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Article Number: 70
• DOI: https://doi.org/10.1214/17-EJP98
• Public URL: https://hull-repository.worktribe.com/output/899204
• Publisher URL: https://projecteuclid.org/euclid.ejp/1505268101#abstract
• Contract Date: Jun 28, 2018