805 research outputs found
A note on a local ergodic theorem for an infinite tower of coverings
This is a note on a local ergodic theorem for a symmetric exclusion process
defined on an infinite tower of coverings, which is associated with a finitely
generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and
Statistic
Universality of trap models in the ergodic time scale
Consider a sequence of possibly random graphs , ,
whose vertices's have i.i.d. weights with a distribution
belonging to the basin of attraction of an -stable law, .
Let , , be a continuous time simple random walk on which
waits a \emph{mean} exponential time at each vertex . Under
considerably general hypotheses, we prove that in the ergodic time scale this
trap model converges in an appropriate topology to a -process. We apply this
result to a class of graphs which includes the hypercube, the -dimensional
torus, , random -regular graphs and the largest component of
super-critical Erd\"os-R\'enyi random graphs
A simple renormalization flow for FK-percolation models
We present a setup that enables to define in a concrete way a renormalization
flow for the FK-percolation models from statistical physics (that are closely
related to Ising and Potts models). In this setting that is applicable in any
dimension of space, one can interpret perturbations of the critical
(conjectural) scaling limits in terms of stationary distributions for rather
simple Markov processes on spaces of abstract discrete weighted graphs.Comment: 12 pages, to appear in the Jean-Michel Bismut 65th anniversary volum
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