Condensation of the Invariant Measures of the Supercritical Zero Range Processes

For α ≥ 1 , let g : N → R + be given by g ( 0 ) = 0 , g ( 1 ) = 1 , g ( k ) = ( k / k - 1 ) α , k ≥ 2 . Consider the homogeneous zero range process on a discrete set in which a particle jumps from a site x , occupied by k particles, to site y with rate g ( k ) p ( y - x ) for some fixed probability...

Full description

Saved in:
Bibliographic Details
Published in:Journal of statistical physics 2024-06, Vol.191 (6), Article 71
Main Author: Xu, Tiecheng
Format: Article
Language:English
Subjects:
Invariants
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For α ≥ 1 , let g : N → R + be given by g ( 0 ) = 0 , g ( 1 ) = 1 , g ( k ) = ( k / k - 1 ) α , k ≥ 2 . Consider the homogeneous zero range process on a discrete set in which a particle jumps from a site x , occupied by k particles, to site y with rate g ( k ) p ( y - x ) for some fixed probability p : Z → [ 0 , 1 ] . Armendáriz and Loulakis (Probab Theory Relat Fields 145:175–188, 2009, https://doi.org/10.1007/s00440-008-0165-7 ) proved a strong form of the equivalence of ensembles for the invariant measure of the supercritical zero range process with α > 2 . We generalize their result to all α ≥ 1 .
ISSN:1572-9613
0022-4715
1572-9613
DOI:10.1007/s10955-024-03287-8