Seminario di Probabilità e Finanza Matematica: Hitting times asymptotics for hard-core interaction on finite graphs and applications to random-access networks

Lunedì 30 Novembre 2015, ore 16.30 - Aula 1BC45 - Alessandro Zocca


Seminario di Probabilità e Finanza Matematica

Lunedì 30 Novembre 2015 alle ore 16.30 in Aula 1BC45, Alessandro Zocca (TU Eindhoven) terrà una conferenza dal titolo "Hitting times asymptotics for hard-core interaction on finite graphs and applications to random-access networks".

We consider the hard-core model on finite graphs, which is a stochastic model for particles that dynamically interact in a finite volume subject to hard-core constraints. This model can be used to describe the dynamics of random-access networks, where, due to wireless interference, active users prevent other nearby users from simultaneous activity. In order to gain insight in the network performance and starvation phenomena, we examine the behavior of the first hitting times between maximum-occupancy configurations and mixing times. For this purpose it is convenient to look at the same model in the framework of Friedlin-Wentzell Markov chains with Metropolis transition probabilities. In this context, the high-fugacity regime in which we are interested corresponds to the low-temperature limit and the maximum-occupancy configurations are the stable states of the corresponding energy landscape. We will illustrate how we extended the pathwise approach beyond the classical metastability setting in order to study, for instance, the tunneling time between stable states. For some specific graphs of interest, e.g. grid graphs and triangular grid graphs, we will show by means of a novel combinatorial method how the order-of magnitude of the tunneling time between the two stable states depends on the size of the lattice and on the boundary conditions. After having discussed some applications of our results to random-access networks, we will then focus on the Widom-Rowlison model on finite graphs which, besides providing another example where our generalized framework can be used, is also instrumental to study multi-channel random-access networks.
(This talk is based on joint work with Sem C. Borst, Johan S.H. van Leewaarden and Francesca R. Nardi)