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.
Hitting Time Asymptotics for Hard-Core Interactions on Grids / Nardi, F.R.; Zocca, A; Borst, S.C.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 162:(2016), pp. 522-576. [10.1007/s10955-015-1391-x]
Hitting Time Asymptotics for Hard-Core Interactions on Grids
NARDI, FRANCESCA ROMANA;
2016
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.File | Dimensione | Formato | |
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