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 language | English |
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Pages (from-to) | 522-576 |
Number of pages | 55 |
Journal | Journal of Statistical Physics |
Volume | 162 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2016 |
Externally published | Yes |
Keywords
- Finite grid graphs
- Hard-core model
- Hitting times
- Low temperature
- Metropolis Markov chains
- Mixing times