# Recent progress on Bernoulli convolutions

• ### Péter P. Varjú

University of Cambridge, UK

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## 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 $\Sigma ± \lambda^n$, where ± are independent fair coin-tosses. This paper surveys recent progress on our understanding of the regularity properties of these measures.