Comptes Rendus
Dynamical systems/Probability theory
On the CLT for rotations and BV functions
Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 212-215.

Let xx+α be a rotation on the circle and let φ be a step function. Denote by φn(x) the ergodic sums j=0n1φ(x+jα). 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 φn/φn2 is asymptotically Gaussian for n in a set of density 1.

Soient xx+α une rotation sur le cercle, φ une fonction en escalier et φn(x) les sommes ergodiques j=0n1φ(x+jα). 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 φn/φn2 est asymptotiquement gaussien pour n dans un ensemble de densité 1.

Published online:
DOI: 10.1016/j.crma.2019.01.008

Jean-Pierre Conze 1; Stéphane Le Borgne 1

1 Université de Rennes, CNRS, IRMAR, UMR 6625, 35000 Rennes, France
     author = {Jean-Pierre Conze and St\'ephane Le Borgne},
     title = {On the {CLT} for rotations and {BV} functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {212--215},
     publisher = {Elsevier},
     volume = {357},
     number = {2},
     year = {2019},
     doi = {10.1016/j.crma.2019.01.008},
     language = {en},
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%A Stéphane Le Borgne
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Jean-Pierre Conze; Stéphane Le Borgne. On the CLT for rotations and BV functions. Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 212-215. doi : 10.1016/j.crma.2019.01.008.

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