Metastability of reversible condensed zero range processes on a finite set

Let be the jump rates of an irreducible random walk on a finite set S , reversible with respect to some probability measure m . For α > 1, let be given by g (0) = 0, g (1) = 1, g ( k ) =  ( k / k − 1) α , k  ≥ 2. Consider a zero range process on S in which a particle jumps from a site x , occupie...

Full description

Saved in:
Bibliographic Details
Published in:Probability theory and related fields 2012-04, Vol.152 (3-4), p.781-807
Main Authors: Beltrán, J., Landim, C.
Format: Article
Language:English
Subjects:
Concentrates
Condensation
Economics
Error analysis
Errors
Finance
Insurance
Management
Mathematical analysis
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Metastability
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random walk
Random walk theory
Set theory
Stands
Statistics for Business
Studies
Syntax
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let be the jump rates of an irreducible random walk on a finite set S , reversible with respect to some probability measure m . For α > 1, let be given by g (0) = 0, g (1) = 1, g ( k ) =  ( k / k − 1) α , k  ≥ 2. Consider a zero range process on S in which a particle jumps from a site x , occupied by k particles, to a site y at rate g ( k ) r ( x , y ). Let N stand for the total number of particles. In the stationary state, as , all particles but a finite number accumulate on one single site. We show in this article that in the time scale N 1+ α the site which concentrates almost all particles evolves as a random walk on S whose transition rates are proportional to the capacities of the underlying random walk.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-010-0337-0