Recent progress on Bernoulli convolutions
  The Bernoulli convolution with parameter $\lambda\in(0,1)$ is the measure on $\bf R$ 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. 
P\'eter P. Varj\'u
math.CA math.DS math.PR