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Title:
Bernoulli convolutions for algebraic parameters
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Abstract:
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 $\lambda \lambda > 1/2$, 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.
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