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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 $\lambda\in(1/2,1)$.
@article{10_4007_annals_2019_189_3_9,
author = {P\'eter P. Varj\'u},
title = {On the dimension of {Bernoulli} convolutions for all transcendental parameters},
journal = {Annals of mathematics},
pages = {1001--1011},
publisher = {mathdoc},
volume = {189},
number = {3},
year = {2019},
doi = {10.4007/annals.2019.189.3.9},
mrnumber = {3961088},
zbl = {07097495},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.3.9/}
}
TY - JOUR AU - Péter P. Varjú TI - On the dimension of Bernoulli convolutions for all transcendental parameters JO - Annals of mathematics PY - 2019 SP - 1001 EP - 1011 VL - 189 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.3.9/ DO - 10.4007/annals.2019.189.3.9 LA - en ID - 10_4007_annals_2019_189_3_9 ER -
%0 Journal Article %A Péter P. Varjú %T On the dimension of Bernoulli convolutions for all transcendental parameters %J Annals of mathematics %D 2019 %P 1001-1011 %V 189 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.3.9/ %R 10.4007/annals.2019.189.3.9 %G en %F 10_4007_annals_2019_189_3_9
Péter P. Varjú. On the dimension of Bernoulli convolutions for all transcendental parameters. Annals of mathematics, Tome 189 (2019) no. 3, pp. 1001-1011. doi: 10.4007/annals.2019.189.3.9
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