Paper
Khintchine dichotomy for self-similar measures
Authors
Timothée Bénard, Weikun He, Han Zhang
Abstract
We establish the analogue of Khintchine's theorem for all self-similar probability measures on the real line. When specified to the case of the Hausdorff measure on the middle-thirds Cantor set, the result is already new and provides an answer to an old question of Mahler. The proof consists in showing effective equidistribution in law of expanding upper-triangular random walks on , a result of independent interest.