171 research outputs found
On the dimension of Bernoulli convolutions for all transcendental parameters
The Bernoulli convolution with parameter is
the probability measure supported on that is the law of the random
variable , where the are independent fair coin-tosses.
We prove that for all transcendental .Comment: 11 pages; version accepted for publication in Ann. of Math.;
dedicated to the memory of Jean Bourgain; minor corrections based on
referee's report; results and proofs are unchange
Recent progress on Bernoulli convolutions
The Bernoulli convolution with parameter is the measure on
that is the distribution of the random power series ,
where are independent fair coin-tosses. This paper surveys recent
progress on our understanding of the regularity properties of these measures.Support received from the Royal Society
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