Zobrazeno 1 - 10
of 110
pro vyhledávání: '"MÁTHÉ, ANDRÁS"'
Autor:
Máthé, András, O'Regan, William Lewis
By making use of arithmetic information inequalities, we give a short new proof of the discretised ring theorem for sets of real numbers. Our proof gives a strong quantitative bound. In particular, we show that if $A \subset [1,2]$ is a $(\delta,\sig
Externí odkaz:
http://arxiv.org/abs/2306.02943
Autor:
Keleti, Tamás, Máthé, András
The Kakeya conjecture is generally formulated as one the following statements: every compact/Borel/arbitrary subset of ${\mathbb R}^n$ that contains a (unit) line segment in every direction has Hausdorff dimension $n$; or, sometimes, that every close
Externí odkaz:
http://arxiv.org/abs/2203.15731
We study a variant of the parallel Moser-Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm is consta
Externí odkaz:
http://arxiv.org/abs/2203.05888
Tarski's Circle Squaring Problem from 1925 asks whether it is possible to partition a disk in the plane into finitely many pieces and reassemble them via isometries to yield a partition of a square of the same area. It was finally resolved by Laczkov
Externí odkaz:
http://arxiv.org/abs/2202.01412
We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function. The main too
Externí odkaz:
http://arxiv.org/abs/1605.04877
Publikováno v:
J Eur Math Soc 24 (2022) 4277-4326
Given an action of a group $\Gamma$ on a measure space $\Omega$, we provide a sufficient criterion under which two sets $A, B\subseteq \Omega$ are measurably equidecomposable, i.e., $A$ can be partitioned into finitely many measurable pieces which ca
Externí odkaz:
http://arxiv.org/abs/1601.02958
Publikováno v:
Random Structures Algorithms 51 (2017), no. 2, 275-314
The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant G(n,W) of the Erdos-Renyi random graph. Here we study the clique number of these random graphs. We establish the concentration of the clique
Externí odkaz:
http://arxiv.org/abs/1510.02335
Publikováno v:
Ergodic Th. Dynam. Syst., 39, (2019), 1-18
It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and the condensa
Externí odkaz:
http://arxiv.org/abs/1509.03589
For $0<\alpha<1$ let $V(\alpha)$ denote the supremum of the numbers $v$ such that every $\alpha$-H\"older continuous function is of bounded variation on a set of Hausdorff dimension $v$. Kahane and Katznelson (2009) proved the estimate $1/2 \leq V(\a
Externí odkaz:
http://arxiv.org/abs/1504.04789
Autor:
Máthé, András
Following Davies, Elekes and Keleti, we study measured sets, i.e. Borel sets $B$ in $\mathbb{R}$ (or in a Polish group) for which there is a translation invariant Borel measure assigning positive and \sigma-finite measure to $B$. We investigate which
Externí odkaz:
http://arxiv.org/abs/1504.02765