Metastability for general dynamics with rare transitions : escape time and critical configurations

E.N.M. Cirillo, F.R. Nardi, J. Sohier

Research output: Book/ReportReportAcademic

Abstract

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical Mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical content, we believe that our results are a useful tool to approach metastability for non-Metropolis systems such as Probabilistic Cellular Automata. Keywords: stochastic dynamics, irreversible Markov chains, hitting times, metastability, Freidlin Wentzell dynamics
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages33
Publication statusPublished - 2015

Publication series

NameReport Eurandom
Volume2015002
ISSN (Print)1389-2355

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    Cirillo, E. N. M., Nardi, F. R., & Sohier, J. (2015). Metastability for general dynamics with rare transitions : escape time and critical configurations. (Report Eurandom; Vol. 2015002). Eindhoven: Eurandom.