Seminario di Probabilità e Finanza Matematica: Metastability in condensing zero-range processes

Lunedì 18 Maggio 2015, ore 14:30 - Aula 2BC30 - Stefan Grosskinsky


Seminario di Probabilità e Finanza Matematica

Lunedì 18 Maggio 2015 alle ore 14:30 in Aula 2BC30 il Prof. Stefan Grosskinsky (Mathematics Institute, University of Warwick) terrà un seminario dal titolo"Metastability in condensing zero-range processes"

We consider a zero-range process with jump rates decreasing with the occupation number, which is known to exhibit a condensation phenomenon where a finite fraction of all particles concentrates on a single lattice site. We derive a scaling limit for the asymptotic stationary dynamics of the condensate location in the thermodynamic limit on a one-dimensional torus. Our proof follows previously developed methods using potential theory and a martingale approach, which have been applied to zero-range processes on finite lattices. The main challenge and novelty of our paper arises from the absence of attractor states which complicates the proof of equilibration within metastable wells and requires a coupling argument to get uniform bounds on exit rates from wells.
This is joint work with Ines Armendariz and Michalis Loulakis.