Basic Notions: Mike Hochman "Dimension of Bernoulli convolutions"

Thu, 14/05/202016:00-17:15
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Abstract: The Bernoulli convolution with parameter 1/2 < t < 1 is the distribution of the random variable (+/-)t + (+/-)t^2 + (+/-)t^3 + ..., where the sequence of signs +/- form an  unbiased i.i.d. random sequence. This distribution has been studied since the 1930s, and the main problem is to characterize those parameters t for which the distribution is absolutely continuous, or has full dimension. In these talks I will review the history and recent developments, leading up to P. Varju's proof a little over a year ago, that for all transcendental parameters the dimension is 1.
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