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Comptes Rendus Mathématique
Volume 357, n° 2
pages 212-215 (février 2019)
Doi : 10.1016/j.crma.2019.01.008
Received : 13 July 2018 ;  accepted : 25 January 2019
On the CLT for rotations and BV functions
Sur le TCL pour les rotations et les fonctions BV
 

Jean-Pierre Conze , Stéphane Le Borgne
 Université de Rennes, CNRS, IRMAR, UMR 6625, 35000 Rennes, France 

Abstract

Let   be a rotation on the circle and let φ be a step function. Denote by   the ergodic sums  . For α in a class containing the rotations with bounded partial quotients and under a Diophantine condition on the discontinuities of φ , we show that   is asymptotically Gaussian for n in a set of density 1.

The full text of this article is available in PDF format.
Résumé

Soient   une rotation sur le cercle, φ une fonction en escalier et   les sommes ergodiques  . Pour α dans une classe contenant les rotations à quotients partiels bornés et sous une condition diophantienne sur les discontinuités de φ , nous montrons que   est asymptotiquement gaussien pour n dans un ensemble de densité 1.

The full text of this article is available in PDF format.


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