45 citations · 191 across the 18 of their papers we have counts for
7 papers · 1 filter
Self-similar sets and measures on the line
Péter P. Varjú
We discuss the problem of determining the dimension of self-similar sets and measures on . We focus on the developments of the last four years. At the end of the paper,…
Fourier decay of self-similar measures and self-similar sets of uniqueness
Péter P. Varjú, Han Yu
In this paper, we investigate the Fourier transform of self-similar measures on R. We provide quantitative decay rates of Fourier transform of some self-similar measures. Our metho…
On the dimension of Bernoulli convolutions for all transcendental parameters
Péter P. Varjú
The Bernoulli convolution with parameter is the probability measure supported on that is the law of the random variable , where the …
On the dimension of Bernoulli convolutions
Emmanuel Breuillard, Péter P. Varjú
The Bernoulli convolution with parameter is the probability measure that is the law of the random variable , where the signs are independent u…
Recent progress on Bernoulli convolutions
Péter P. Varjú
The Bernoulli convolution with parameter is the measure on that is the distribution of the random power series , where are independent fair co…
Absolute continuity of Bernoulli convolutions for algebraic parameters
Péter P. Varjú
We prove that Bernoulli convolutions are absolutely continuous provided the parameter lambda is an algebraic number sufficiently close to 1 depending on the Mahler measure of lambd…
Entropy of Bernoulli convolutions and uniform exponential growth for linear groups
Emmanuel Breuillard, Péter P. Varjú
The exponential growth rate of non polynomially growing subgroups of is conjectured to admit a uniform lower bound. This is known for non-amenable subgroups, while for amena…