Countable Markov shifts with exponential mixing

2024/03/04 by Mike Todd, Todd, Mike, Boyuan Zhao +1
Computer Science · Mathematics · #37A25 #37B10 #37D05 #37D25 #Advanced Topology and Set Theory #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2403.02092

openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a set of equivalent conditions for a potential on a Countable Markov Shift to have strong positive recurrence, which is also equivalent to having exponential decay of correlations. A key ingredient of our proofs is quantifying how the shift behaves at its boundary.

Related

• Recurrence rates for shifts of finite type
• Pressure Inequalities for Gibbs Measures of Countable Markov Shifts
• Effective intrinsic ergodicity for countable state Markov shifts
• Strong positive recurrence and exponential mixing for diffeomorphisms
• d-continuity for countable state shifts