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arXiv · 0905.3850

Convolutions of Cantor measures without resonance

Fedor Nazarov·Yuval Peres·Pablo Shmerkin
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Abstract

Denote by $μ_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty ω_j a^j$, where $P(ω_j=0)=P(ω_j=1)=1/2$ and all the choices are independent. For $0 1$ and $\log (1/3) /\log (1/4)$ is irrational.

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Fedor Nazarov, Yuval Peres, Pablo Shmerkin. 2009-05-23. Convolutions of Cantor measures without resonance. https://arxiv.org/abs/0905.3850

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