Projections of Gibbs States for Hölder Potentials

Mark Stephens Piraino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We give a short proof that the projection of a Gibbs state for a Hölder continuous potential on a mixing shift of finite type under a 1-block fiber-wise mixing factor map has a Hölder continuous g function. This improves a number of previous results. The key insight in the proof is to realize the measure of a cylinder set in terms of positive operators and use cone techniques.

Original languageEnglish (US)
Pages (from-to)952-961
Number of pages10
JournalJournal of Statistical Physics
Issue number5
StatePublished - Mar 1 2018


  • Hidden Markov measures
  • Hilbert’s metric
  • Projections of Gibbs states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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