Concentration inequalities and rates of convergence of the ergodic theorem for countable shifts with Gibbs measures

DOI10.1080/10236198.2021.2000970zbMath1479.37023OpenAlexW3212983448WikidataQ114099708 ScholiaQ114099708MaRDI QIDQ5016812

Hugo Nieto Loredo, Cesar Maldonado, Humberto Muñiz

Publication date: 13 December 2021

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2021.2000970

zbMATH Keywords

rates of convergencesymbolic dynamicsergodic theoryGibbs measuresconcentration inequalitiescountable shifts

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Stability theory for difference equations (39A30)

Cites Work

• Unnamed Item
• Unnamed Item
• Large deviations and rates of convergence in the Birkhoff ergodic theorem: from Hölder continuity to continuity
• Spectral gap and transience for Ruelle operators on countable Markov shifts
• Expanding measures
• Optimal concentration inequalities for dynamical systems
• Exponential inequalities for dynamical measures of expanding maps of the interval
• Annealed and quenched limit theorems for random expanding dynamical systems
• Moment bounds and concentration inequalities for slowly mixing dynamical systems
• Concentration bounds for entropy estimation of one-dimensional Gibbs measures
• LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS
• Rates of mixing for potentials of summable variation
• Existence of Gibbs measures for countable Markov shifts
• Thermodynamic formalism for countable Markov shifts
• Fluctuation bounds for entropy production estimators in Gibbs measures
• Gaussian concentration bound for potentials satisfying Walters condition with subexponential continuity rates
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Gibbs states on the symbolic space over an infinite alphabet

This page was built for publication: Concentration inequalities and rates of convergence of the ergodic theorem for countable shifts with Gibbs measures