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Seminario di Probabilità: “Hitting Time Asymptotics for Hard-Core Interactions on Grids”

Lunedì 20 Marzo 2017, ore 14:15 - Aula 1BC45 - Francesca Nardi

ARGOMENTI: Seminari

Lunedì 20 Marzo 2017 alle ore 14:15 in Aula 1BC45, Francesca Nardi (Università di Firenze) terrà un seminario dal titolo “Hitting Time 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 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.
Work in collaboration with A. Zocca S. C. Borst.