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Bernoulli convolutions for algebraic parameters

Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 12, 2015 (01:30 PM PDT - 02:20 PM PDT)
Speaker(s): Peter Varju (University of Cambridge)
Location: MSRI: Simons Auditorium
  • processes on random variables

  • singular measures

  • absolutely continuous measure

  • Hausdorff dimension

  • packing dimension

  • Cantor set

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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.

23522?type=thumb Varju. Notes 185 KB application/pdf Download
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