Ergodicity for infinite particle systems with locally conserved quantities

J. Inglis, M. Neklyudov, B. Zegarlinski

Published 2010-02-01, updated 2010-08-16Version 2

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.