SPEAKER:
Sander Dommers
AFFILIATION:
University of Bochum
TITLE:
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 goeas to 0 as N goeas 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.