45 citations · 191 across the 18 of their papers we have counts for
22 papers
Exponential multiple mixing for commuting automorphisms of a nilmanifold
Timothée Bénard, Péter P. Varjú
Let and be an action of by automorphisms on a compact nilmanifold . We a…
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,…
On the multiplicative group generated by two primes in
Péter P. Varjú
We study the action of the multiplicative group generated by two prime numbers in . More specifically, we study returns to the set $([-Q^\varepsilon,Q^\vare…
Self-similar measures associated to a homogeneous system of three maps
Ariel Rapaport, Péter P. Varjú
We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on and other more general IFS's. We e…
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…
Mixing time of the Chung--Diaconis--Graham random process
Sean Eberhard, Péter P. Varjú
Define on by , where the steps are chosen independently at random from . The mixing time of this random walk…
Cut-off phenomenon for the ax+b Markov chain over a finite field
Emmanuel Breuillard, Péter P. Varjú
We study the Markov chain on a finite field , where is fixed and are independent and identically distributed random vari…
On the Lehmer conjecture and counting in finite fields
Emmanuel Breuillard, Péter P. Varjú
We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.
Irreducibility of random polynomials of large degree
Emmanuel Breuillard, Péter P. Varjú
We consider random polynomials with independent identically distributed coefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind zeta functions, we prove that su…
Expansion of coset graphs of PSL_2(F_p)
Péter P. Varjú
Let be a finite group and let be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are and a coset i…
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…
The structure theory of Nilspaces III: Inverse limit representations and topological dynamics
Yonatan Gutman, Freddie Manners, Péter P. Varjú
This paper forms the third part of a series by the authors [GMV1,GMV2] concerning the structure theory of nilspaces. A nilspace is a compact space together with closed collecti…
The structure theory of Nilspaces II: Representation as nilmanifolds
Yonatan Gutman, Freddie Manners, Péter P. Varjú
This paper forms the second part of a series by the authors [GMV1,GMV3] concerning the structure theory of nilspaces of Antolín Camarena and Szegedy. A nilspace is a compact space…
The structure theory of Nilspaces I
Yonatan Gutman, Freddie Manners, Péter P. Varjú
This paper forms the first part of a series by the authors [GMV2,GMV3] concerning the structure theory of nilspaces of Antolín Camarena and Szegedy. A nilspace is a compact space $…
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…
Random walks in the group of Euclidean isometries and self-similar measures
Elon Lindenstrauss, Péter P. Varjú
We study products of random isometries acting on Euclidean space. Building on previous work of the second author, we prove a local limit theorem for balls of shrinking radius with…
Diophantine property in the group of affine transformations of the line
Péter Pál Varjú
We investigate the Diophantine property of a pair of elements in the group of affine transformations of the line. We say that a pair of elements g_1,g_2 in this group is Diophantin…
Random walks in Euclidean space
Péter Pál Varjú
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the…
Expansion in , square-free
Péter P. Varjú
Let S be a fixed symmetric finite subset of SL_d(O_K) that generates a Zariski dense subgroup of SL_d(O_K) when we consider it as an algebraic group over Q by restriction of scalar…