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arXiv · 1810.08905

On the dimension of Bernoulli convolutions for all transcendental parameters

Péter P. Varjú
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Abstract

The Bernoulli convolution $\nu_\lambda$ with parameter $\lambda\in(0,1)$ is the probability measure supported on $\mathbf{R}$ that is the law of the random variable $\sum\pm\lambda^n$, where the $\pm$ are independent fair coin-tosses. We prove that $\dim\nu_\lambda=1$ for all transcendental $\lambda\in(1/2,1)$.

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Péter P. Varjú. 2018-10-21. On the dimension of Bernoulli convolutions for all transcendental parameters. https://doi.org/10.4007/annals.2019.189.3.9

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