Growth of normalizing sequences in limit theorems for conservative maps

DOI10.1214/18-ECP192zbMath1406.60039arXiv1803.11472MaRDI QIDQ1725491

Sébastien Gouëzel

Publication date: 14 February 2019

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Abstract: We consider normalizing sequences that can give rise to nondegenerate limittheorems for Birkhoff sums under the iteration of a conservative map. Mostclassical limit theorems involve normalizing sequences that are polynomial,possibly with an additional slowly varying factor. We show that, ingeneral, there can be no nondegenerate limit theorem with a normalizingsequence that grows exponentially, but that there are examples where itgrows like a stretched exponential, with an exponent arbitrarily close to 1.

Full work available at URL: https://arxiv.org/abs/1803.11472

zbMATH Keywords

normalizationlimit theoremstransfer operatorinfinite ergodic theoryrenewal Markov chain

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Nonsingular (and infinite-measure preserving) transformations (37A40)

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Related Items (2)

Flexibility of statistical properties for smooth systems satisfying the central limit theorem ⋮ Growth of normalizing sequences in limit theorems for conservative maps

Uses Software

• Ergodic theory
• Archive Formal Proofs

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