Limit theorems for numbers of multiple returns in non-conventional arrays

DOI10.1017/etds.2021.33zbMath1482.60038arXiv1910.01439OpenAlexW3211417299WikidataQ113858342 ScholiaQ113858342MaRDI QIDQ5027313

Yuri Kifer

Publication date: 4 February 2022

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.01439

zbMATH Keywords

multiple returnsgeometric and Poisson distributionsnon-conventional sums

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Discrete-time Markov processes on general state spaces (60J05) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35)

Cites Work

• Nonconventional Poisson limit theorems
• Poisson and compound Poisson approximations in conventional and nonconventional setups
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Ergodic theorems for nonconventional arrays and an extension of the Szemerédi theorem
• Geometric law for numbers of returns until a hazard under \(\varphi\)-mixing
• A functional CLT for nonconventional polynomial arrays
• Geometric law for multiple returns until a hazard
• Nonconventional Limit Theorems and Random Dynamics
• Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C ² - Transformations
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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