Ergodicity for infinite particle systems with locally conserved quantities
Probability
2010-08-17 v2 Mathematical Physics
math.MP
Abstract
We analyse certain degenerate infinite dimensional sub-elliptic generators, and obtain estimates on the long-time behaviour of the corresponding Markov semigroups that describe a certain model of heat conduction. In particular, we establish ergodicity of the system for a family of invariant measures, and show that the optimal rate of convergence to equilibrium is polynomial. Consequently, there is no spectral gap, but a Liggett-Nash type inequality is shown to hold.
Cite
@article{arxiv.1002.0282,
title = {Ergodicity for infinite particle systems with locally conserved quantities},
author = {J. Inglis and M. Neklyudov and B. Zegarlinski},
journal= {arXiv preprint arXiv:1002.0282},
year = {2010}
}
Comments
34 pages; introduction rewritten, minor corrections, references added