## Bernoulli convolutions

#### Peter Varju (University of Cambridge)

Frank Adams 1,

The Bernoulli convolution with parameter $$\lambda$$ is the law of the random variable: $$\sum X_i \lambda_i$$, where $$X_i$$ are independent unbiased +1/ − 1 valued random variables. If $$\lambda < 1/2$$, then the Bernoulli convolution is singular and is supported on a Cantor set. If $$1 > \lambda > 1/2$$, the question whether the Bernoulli convolution is singular or a.c. is a very interesting open problem. I will talk about some recent results about this problem, some of which are joint work with Emmanuel Breuillard.