Hitting times asymptotics for hard-core interactions on grids
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
Cite
@article{arxiv.1503.06757,
title = {Hitting times asymptotics for hard-core interactions on grids},
author = {Francesca R. Nardi and Alessandro Zocca and Sem C. Borst},
journal= {arXiv preprint arXiv:1503.06757},
year = {2016}
}