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.
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.
Accepted:
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Jean-Pierre Conze 1; Stéphane Le Borgne 1
@article{CRMATH_2019__357_2_212_0, 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}, }
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.01.008/
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