3 citations · 6 across the 14 of their papers we have counts for
15 papers
Galois groups of random polynomials of large degree
Guy Blachar, Emmanuel Breuillard, Gady Kozma
We study random polynomials of the form , where are independent, uniformly bounded integer-valued random variables, and $ω_1…
Edge-regular graphs with non-negative curvature have polynomial growth
Guy Blachar, Hervé Pajot, Justin Salez
A long-standing conjecture in the emerging discrete Bakry-Émery theory asserts that bounded-degree graphs satisfying have polynomial growth. In the present…
Small entropy doubling for random walks and polynomial growth
Guy Blachar
Gromov's theorem states that a finitely generated group has polynomial growth if and only if it is virtually nilpotent. A key ingredient in its proof is the small doubling property…
Phase transition for recurrence of stationary random walks on lamplighter groups
Itai Benjamini, Guy Blachar, Ariel Yadin
We introduce and study a class of random walks on lamplighter groups , where is a nontrivial finitely generated group and is an infinite finitely generated group, c…
The speed of random walks on semigroups
Guy Blachar, Be'eri Greenfeld
We construct, for each real number , a random walk on a finitely generated semigroup whose speed exponent is . We further show that the speed function of a random…
Mixability of finite groups
Gideon Amir, Guy Blachar, Subhajit Ghosh +1
Say that a finite group is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on . We present conditions and obstr…
Profinite rigidity of lamplighter groups
Guy Blachar
We show that the lamplighter groups , where is prime and is a positive integer, are profinitely rigid.
Rank-stability of polynomial equations
Tomer Bauer, Guy Blachar, Be'eri Greenfeld
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approxi…
Lipschitz harmonic functions on vertex-transitive graphs
Gideon Amir, Guy Blachar, Maria Gerasimova +1
We prove that every locally finite vertex-transitive graph admits a non-constant Lipschitz harmonic function.
Semiassociative algebras over a field
Guy Blachar, Darrell Haile, Eliyahu Matzri +2
An associative central simple algebra is a form of matrices, because a maximal étale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to ex…
Probabilistic Laws on Infinite Groups
Gideon Amir, Guy Blachar, Maria Gerasimova +1
We study the probability that certain laws are satisfied on infinite groups, focusing on elements sampled by random walks. For several group laws, including the metabelian one, we…
A Law of Iterated Logarithm on Lamplighter Diagonal Products
Gideon Amir, Guy Blachar
We prove a Law of Iterated Logarithm for random walks on a family of diagonal products constructed by Brieussel and Zheng (2021). This provides a wide variety of new examples of La…
Modules and Lie Semialgebras over Semirings with a Negation Map
Guy Blachar
In this article, we present the basic definitions of modules and Lie semialgebras over semirings with a negation map. Our main example of a semiring with a negation map is ELT alge…
ELT Linear Algebra II
Guy Blachar, Erez Sheiner
This paper is a continuation of [arXiv:1603.02204]. Exploded layered tropical (ELT) algebra is an extension of tropical algebra with a structure of layers. These layers allow us to…
ELT Linear Algebra
Guy Blachar, Erez Sheiner
Exploded layered tropical (ELT) algebra is an extension of tropical algebra with a structure of layers. These layers allow us to use classical algebraic results in order to easily…