Existence of the Zero Range Process and a Deposition Model with Superlinear Growth Rates

We give a construction of the zero range and bricklayers' processes in the totally asymmetric, attractive case. The novelty is that we allow jump rates to grow exponentially. Earlier constructions have permitted at most linearly growing rates. We also show the invariance and extremality of a na...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of probability 2007-07, Vol.35 (4), p.1201-1249
Main Authors: Balázs, M., Rassoul-Agha, F., Seppäläinen, T., Sethuraman, S.
Format: Article
Language:English
Subjects:
60K35
82C41
Antiparticles
bricklayer’s
Bricklaying
Bricks
construction of dynamics
Ergodic theory
ergodicity of dynamics
Exact sciences and technology
General topics
Integers
Limit theorems
Markov processes
Mathematical analysis
Mathematical moments
Mathematics
Particle interactions
Poisson process
Probability
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Semigroups
Studies
superlinear jump rates
Zero range
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:We give a construction of the zero range and bricklayers' processes in the totally asymmetric, attractive case. The novelty is that we allow jump rates to grow exponentially. Earlier constructions have permitted at most linearly growing rates. We also show the invariance and extremality of a natural family of i.i.d. product measures indexed by particle density. Extremality is proved with an approach that is simpler than existing ergodicity proofs.
ISSN:0091-1798
2168-894X
DOI:10.1214/009117906000000971