Hitting time asymptotics for hard-core interactions on grids

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Abstract

We consider the hard-core model with Metropolis transition probabilities on finite grid graphs and investigate the asymptotic behavior of the first hitting time between its two maximum-occupancy configurations in the low-temperature regime. In particular, we show how the order-of-magnitude of this first hitting time depends on the grid sizes and on the boundary conditions by means of a novel combinatorial method. Our analysis also proves the asymptotic exponentiality of the scaled hitting time and yields the mixing time of the process in the low-temperature limit as side-result. In order to derive these results, we extended the model-independent framework in [27] for first hitting times to allow for a more general initial state and target subset. Keywords: hard-core model; hitting times; Metropolis Markov chains; finite grid graphs; mixing times; low temperature.
Original languageEnglish
Pages (from-to)522-576
JournalJournal of Statistical Physics
Volume162
Issue number2
Early online date8 Oct 2015
DOIs
Publication statusPublished - Jan 2016

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