English

Effective intrinsic ergodicity for countable state Markov shifts

Dynamical Systems 2021-12-03 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2112.01186,
  title  = {Effective intrinsic ergodicity for countable state Markov shifts},
  author = {René Rühr and Omri Sarig},
  journal= {arXiv preprint arXiv:2112.01186},
  year   = {2021}
}
R2 v1 2026-06-24T08:01:26.079Z