Title
Constant-length random substitutions and gibbs measures
Author
Maldonado Ahumada, César Octavio
Trejo Valencia, Liliana
Ugalde, Edgardo
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 substitutions rule, the existence of a unique process which remains invariant under the substitution, and which exhibits a 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 end up the paper by studying a class of substitutions whose invariant state is the unique Gibbs measure for a hierarchical two-body interaction."
Publication date
2018Publication type
articleDOI
https://doi.org/10.1007/s10955-018-2010-4Knowledge area
MATEMÁTICASEditor
SpringerKeywords
Gibbs measuresRandom substitutions
Projective convergence