The evolution of the condensate in the zero range process

Acronym

P_ZRP-COND

Consortium Coordinator

Beltran Ramirez, Johel Victorino

Start Date

March 1, 2016

End Date

February 27, 2017

Status

https://purl.org/pe-repo/concytec/estadoProyecto#concluido

Tipo de proyecto

https://purl.org/pe-repo/ocde/tipoProyecto#investigacionBasica

Description

The zero range process is an interacting particle system in which many indistinguishable particles occupy sites on a lattice. Each lattice site may contain an integer number of particles and these particles hop between neighboring sites with a rate that depends on the number of particles at the site of departure. In this project we consider a zero range process on a finite (fixed) lattice and in which the rates decrease to a positive constant. Under some conditions on the velocity of convergence of the rates, a condensation phenomenon occurs: the stationary measure concentrates on configurations of particles in which all but a few number of particles occupy one single site. The site with maximal occupancy is called the condensate. It has been studied in [7] the asymptotic evolution of the condensate: Fix an initial configuration of N particles with the majority of them located at one site and observe the position X^N_t of the condensate at each time t. Then, as N goes to infinity, it is proved in [7] that the law of the path X^N converges to the law of a Markov chain on the set o sites. Such result has been obtained under the assumption of reversibility. The objective of this project is to use the recent results obtained in [4] and [6] to extend the result in [7] to the nonreversible case.

Keywords

Proceso de rango cero

;

Condensación

;

Procesos estocásticos

;

Evolución temporal

Área de conocimiento

Natural sciences

Campo OCDE

https://purl.org/pe-repo/ocde/ford#1.01.03