Special Analysis Seminar

Bernoulli convolutions for algebraic parameters

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. Recent papers of Hochman and Shmerkin prove that the set of $\lambda$'s such that the measure is singular is of Hausdorff dimension 0. I will discuss the problem for parameters $\lambda$ that are algebraic. Work in progress, joint with Emmanuel Breuillard.

Date & Time

May 08, 2015 | 3:00pm – 4:00pm

Location

S-101

Speakers

Peter Varju

Affiliation

University of Cambridge

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