Uniform lower bounds on the dimension of Bernoulli convolutions

In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The Bernoulli convolution measure μλ is the probability measure cor...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2022-02, Vol.395, p.108090, Article 108090
Main Authors: Kleptsyn, V., Pollicott, M., Vytnova, P.
Format: Article
Language:English
Subjects:
Bernoulli convolutions
Dimension of stationary measures
Dynamical Systems
Iterated function schemes
Mathematical Physics
Mathematics
Probability
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Summary:In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The Bernoulli convolution measure μλ is the probability measure corresponding to the law of the random variableξ=∑k=0∞ξkλk, where ξk are i.i.d. random variables assuming values −1 and 1 with equal probability and 12
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.108090