# Seminario di Probabilità e Finanza Matematica: “Metastability in the reversible inclusion process”

## Giovedì 24 Novembre 2016, ore 14:30 - Aula 2BC30 - Sander Dommers

ARGOMENTI: Seminari

Giovedì 24 Novembre 2016 alle 14:30 in Aula 2BC30, Sander Dommers (University of Bochum) terrà un semianrio dal titolo “Metastability in the reversible inclusion process”.

Abstract
In the reversible inclusion process with $N$ particles on a finite graph each particle at a site $x$ jumps to site $y$ at rate $(d+\eta_y) r(x,y)$, where $d$ is a diffusion parameter, $\eta_y$ is the number of particles on site $y$ and $r(x,y)$ is the jump rate from $x$ to $y$ of an underlying reversible random walk.
When the diffusion $d$ goes to $0$ as $N$ goes to infinity, the particles cluster together to form a condensate. It turns out that these condensates only form on the sites where the underlying random walk spends the most time. Once such a condensate is formed the particles stick together and the condensate performs a random walk itself on much longer timescales, which can be seen as metastable behavior.
We study the rates at which the condensate jumps and show that in the reversible case there are three time scales on which these jumps occur depending on how far (in graph distance) the sites are from each other. This generalizes work by Grosskinsky, Redig and Vafayi who study the symmetric case where only one timescale is present. Our analysis is based on potential theory and the martingale approach by Beltrán and Landim.
This is joint work with Alessandra Bianchi and Cristian Giardinà.