Effective intrinsic ergodicity for countable state Markov shifts

René Rühr, Omri Sarig

Research output: Contribution to journalArticlepeer-review


For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for subshifts of finite type, due to Kadyrov. We provide a similar bound for equilibrium measures of strongly positively recurrent potentials, in terms of the pressure difference. For measures with nearly maximal entropy, we have new, and sharp, bounds. The strong positive recurrence condition is necessary.

Original languageEnglish
Pages (from-to)679-735
Number of pages57
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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