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 language | English |
---|---|
Pages (from-to) | 522-576 |
Journal | Journal of Statistical Physics |
Volume | 162 |
Issue number | 2 |
Early online date | 8 Oct 2015 |
DOIs | |
Publication status | Published - Jan 2016 |