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Uniform lower bounds on the dimension of Bernoulli convolutions.
- Source :
-
Advances in Mathematics . Feb2022, Vol. 395, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- 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 μ λ is the probability measure corresponding to the law of the random variable ξ = ∑ k = 0 ∞ ξ k λ k , where ξ k are i.i.d. random variables assuming values −1 and 1 with equal probability and 1 2 < λ < 1. In particular, for Bernoulli convolutions we give a uniform lower bound dim H (μ λ) ≥ 0.96399 for all 1 2 < λ < 1. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FRACTAL dimensions
*PROBABILITY measures
*RANDOM variables
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 395
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 154658067
- Full Text :
- https://doi.org/10.1016/j.aim.2021.108090