Hitting Time Asymptotics for Hard-Core Interactions on Grids

F. R. Nardi, A. Zocca*, S. C. Borst

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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 Manzo et al. (J Stat Phys 115(1/2):591–642, 2004) for first hitting times to allow for a more general initial state and target subset.

Original languageEnglish
Pages (from-to)522-576
Number of pages55
JournalJournal of Statistical Physics
Volume162
Issue number2
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Finite grid graphs
  • Hard-core model
  • Hitting times
  • Low temperature
  • Metropolis Markov chains
  • Mixing times

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