A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory

DOI10.3934/dcdss.2017016zbMath1385.37029arXiv1604.08252OpenAlexW3100724202MaRDI QIDQ504039

Sabrina Kombrink, Marc Kesseböhmer

Publication date: 25 January 2017

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08252

zbMATH Keywords

renewal theoryinfinite alphabet subshiftRuelle-Perron-Frobenius operator

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Renewal theory (60K05)

Related Items (6)

Spectral asymptotics of Kreĭn-Feller operators for weak Gibbs measures on self-conformal fractals with overlaps ⋮ Pressure metrics for cusped Hitchin components ⋮ Hitchin representations of Fuchsian groups ⋮ Renewal theorems and their application in fractal geometry ⋮ Renewal theorems for processes with dependent interarrival times ⋮ Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations

Cites Work

• Fractal curvature measures and Minkowski content for self-conformal subsets of the real line
• Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
• Minkowski content and fractal Euler characteristic for conformal graph directed systems
• A complex Ruelle-Perron-Frobenius theorem and two counterexamples
• Applied Probability and Queues
• Existence of Gibbs measures for countable Markov shifts
• Induced topological pressure for countable state Markov shifts
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