Recent progress on Bernoulli convolutions

Abstract

The Bernoulli convolution with parameter $\lambda \in (0,1)$ is the measure on $\mathbf{R}$ that is the distribution of the random power series $\sum \pm {\lambda }^n$, where $\pm$ are independent fair coin-tosses. This paper surveys recent progress on our understanding of the regularity properties of these measures.

arXiv comment21 pages, to appear in the Proceedings of the 7th ECM, Berlin