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. 

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