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arXiv · 2110.09072

Towards Absolutely Continuous Bernoulli Convolutions

Alex Batsis·Tom Kempton
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Abstract

We show how to turn the question of the absolute continuity of Bernoulli convolutions into one of counting the growth of the number of overlaps in the system. When the contraction parameter is a hyperbolic algebraic integer, we turn this question of absolute continuity into a question involving the ergodic theory of cocycles over domain exchange transformations.

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Alex Batsis, Tom Kempton. 2021-10-18. Towards Absolutely Continuous Bernoulli Convolutions. https://arxiv.org/abs/2110.09072

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