RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 4, Pages 733–753 (Mi tvp127)

On the CLT for means under the rotation action. I

M. Weber

Institut de Recherche Mathématique Avancée, Université de Strasbourg

Abstract: We propose a method allowing us to build, for various typical means generated by the action of any given irrational rotation of the circle, examples of $L^2$ functions satisfying the central limit theorem (CLT). We consider, for instance, nonlinear means, and means along the sequence of squares. In the latter case, the circle method of Hardy and Littlewood is used. We also give an example of continuous Gaussian random Fourier series with sample paths satisfying both the CLT and the almost sure CLT.

Keywords: central limit theorem, almost sure central limit theorem, irrational rotations, nonlinear averages, square averages, weighted averages, Gaussian randomization, random Fourier series, circle method.

DOI: https://doi.org/10.4213/tvp127

Full text: PDF file (1553 kB)

English version:
Theory of Probability and its Applications, 2006, 50:4, 631–649

Bibliographic databases:

Revised: 29.03.2005
Language:

Citation: M. Weber, “On the CLT for means under the rotation action. I”, Teor. Veroyatnost. i Primenen., 50:4 (2005), 733–753; Theory Probab. Appl., 50:4 (2006), 631–649

Citation in format AMSBIB
\Bibitem{Web05} \by M.~Weber \paper On the CLT for means under the rotation action.~I \jour Teor. Veroyatnost. i Primenen. \yr 2005 \vol 50 \issue 4 \pages 733--753 \mathnet{http://mi.mathnet.ru/tvp127} \crossref{https://doi.org/10.4213/tvp127} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2331985} \zmath{https://zbmath.org/?q=an:1110.60018} \elib{http://elibrary.ru/item.asp?id=9157510} \transl \jour Theory Probab. Appl. \yr 2006 \vol 50 \issue 4 \pages 631--649 \crossref{https://doi.org/10.1137/S0040585X97982013} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243284300005}