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- Title
Constant-Length Random Substitutions and Gibbs Measures.
- Authors
Maldonado, C.; Trejo-Valencia, L.; Ugalde, E.
- Abstract
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, undermild conditions on the substitution's 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.
- Subjects
FINITE element method; GIBBS phenomenon; MARKOV spectrum; APPROXIMATION theory; MATHEMATICAL symmetry
- Publication
Journal of Statistical Physics, 2018, Vol 171, Issue 2, p269
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-018-2010-4