The weak Bernoulli property for matrix Gibbs states

Mark Piraino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study the ergodic properties of a class of measures on for which, where is a collection of matrices. The measure is called a matrix Gibbs state. In particular, we give a sufficient condition for a matrix Gibbs state to have the weak Bernoulli property. We employ a number of techniques to understand these measures, including a novel approach based on Perron-Frobenius theory. We find that when is an even integer the ergodic properties of are readily deduced from finite-dimensional Perron-Frobenius theory. We then consider an extension of this method to 0]]> using operators on an infinite- dimensional space. Finally, we use a general result of Bradley to prove the main theorem.

Original languageEnglish (US)
Pages (from-to)2219-2238
Number of pages20
JournalErgodic Theory and Dynamical Systems
Issue number8
StatePublished - Aug 1 2020


  • Matrix equilibrium states
  • Symbolic dynamics
  • Thermodynamic formalism
  • Weak Bernoulli property

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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