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arXiv · 1712.00586

Constant-length random substitutions and Gibbs measures

Cesar Maldonado·Liliana Trejo-Valencia·Edgardo Ugalde
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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.

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Cesar Maldonado, Liliana Trejo-Valencia, Edgardo Ugalde. 2017-12-02. Constant-length random substitutions and Gibbs measures. https://doi.org/10.1007/s10955-018-2010-4

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