Constant-length random substitutions and Gibbs measures
Mathematical Physics
2018-04-04 v1 math.MP
Abstract
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the substitution, and exhibiting polynomial decay of correlations. For constant-length substitutions, we go further by proving that the invariant state is precisely a Gibbs measure which can be obtained as the projective limit of its natural Markovian approximations. We close the paper with a class of substitutions whose invariant state is the unique Gibbs measure for a hierarchical two-body interaction.
Cite
@article{arxiv.1712.00586,
title = {Constant-length random substitutions and Gibbs measures},
author = {Cesar Maldonado and Liliana Trejo-Valencia and Edgardo Ugalde},
journal= {arXiv preprint arXiv:1712.00586},
year = {2018}
}