ERDOS-RENYI LAWS FOR EXPONENTIALLY AND POLYNOMIALLY MIXING DYNAMICAL SYSTEMS

被引：0

作者：

Haydn, Nicolai ^{[1
]}

Nicol, Matthew ^{[2
]}

机构：

[1] Univ Southern Calif, Dept Math, Los Angeles, CA 90007 USA

[2] Univ Houston, Dept Math, Houston, TX 77204 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 08期

基金：

美国国家科学基金会;

关键词：

LARGE DEVIATIONS; LIMIT-THEOREMS;

D O I：

10.1090/proc/16091

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Erdos-Renyi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdos-Renyi type limit laws for Holder observables on dynamical systems modeled by Young Towers with exponential and polynomial tails. This extends earlier results on Erdos-Renyi limit laws to a broad class of dynamical systems with some degree of hyperbolicity.

引用

页码：3415 / 3430

页数：16

共 24 条

[1]

Bryc W., 1993, J. Theoret. Probab., V6, P473

[2] Almost-sure central limit theorems and the Erdos-Renyi law for expanding maps of the interval [J].

Chazottes, JR ;

Collet, P .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :419-441

[3] A generalization of the Erdos-Renyi limit theorem and the corresponding multifractal analysis [J].

Chen, Haibo ;

Yu, Min .

JOURNAL OF NUMBER THEORY, 2018, 192 :307-327

[4] The Hausdorff dimension of level sets described by Erdos-Renyi average [J].

Chen, Haibo ;

Ding, Daoxin ;

Long, Xinghuo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 458 (01) :464-480

[5] A family of chaotic billiards with variable mixing rates [J].

Chernov, N ;

Zhang, HK .

STOCHASTICS AND DYNAMICS, 2005, 5 (04) :535-553

[6] ERDOS-RENYI LAWS [J].

CSORGO, S .

ANNALS OF STATISTICS, 1979, 7 (04) :772-787

[7] EXACT CONVERGENCE RATE IN THE LIMIT-THEOREMS OF ERDOS-RENYI AND SHEPP [J].

DEHEUVELS, P ;

DEVROYE, L ;

LYNCH, J .

ANNALS OF PROBABILITY, 1986, 14 (01) :209-223

[8]

Denker M., 2007, PROBABILITY MATH STA, V27, P139

[9] Erdos-Renyi laws for dynamical systems [J].

Denker, Manfred ;

Nicol, Matthew .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2013, 87 :497-508

[10]

Durrett R., 2010, Probability: Theory and Examples, DOI [10.1017/CBO9780511779398, DOI 10.1017/CBO9780511779398]

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