Comptes Rendus
no. 2
Dynamical systems/Probability theory
On the CLT for rotations and BV functions
Presented by: Jean-François Le Gall
Jean-Pierre Conze 1 ; Stéphane Le Borgne 1
1 Université de Rennes, CNRS, IRMAR, UMR 6625, 35000 Rennes, France
Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 212-215

Let x↦x+α be a rotation on the circle and let φ be a step function. Denote by φn(x) the ergodic sums ∑j=0n−1φ(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/‖φn‖2 is asymptotically Gaussian for n in a set of density 1.

Soient x↦x+α une rotation sur le cercle, φ une fonction en escalier et φn(x) les sommes ergodiques ∑j=0n−1φ(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/‖φn‖2 est asymptotiquement gaussien pour n dans un ensemble de densité 1.

Received:
Accepted:
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 
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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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