Related papers: Virtual Geometricity is Rare

We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup $H$. We further assume…

We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…

We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if $G$ is a virtually compact special hyperbolic group, and $Q\leq G$ is a $K$-quasiconvex…

For any positive integers m and n, the word map (x,y) -> x^m y^n is almost measure preserving on large finite simple groups G.

It was recently proven that all free and many virtually free verbally closed subgroups are algebraically closed in any group. We establish sufficient conditions for a group that is an extension of a free non-abelian group by a group…

For every finite generating set on the integer Heisenberg group H(Z), Pansu showed that the word metric has the large-scale structure of a Carnot-Caratheodory Finsler metric on the real Heisenberg group H(R). We study the properties of…

In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good GIT quotients regardless of…

We consider invariant measures of maps on manifolds whose correlations decay at a sufficient rate and which satisfy a geometric contraction property. We then prove the that the limiting distribution of returns to geometric balls is…

We prove some triviality results for reduced Whitehead groups and reduced unitary Whitehead groups for division algebras over a henselian discrete valuation field whose residue field has virtual cohomological dimension or separable…

The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…

A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite…

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.

In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…

We investigate the problem of reconstructing a set $P\subseteq \mathbb{R}$ of distinct points, where the only information available about $P$ consists of the distances between some of the pairs of points. More precisely, we examine which…

We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…

This paper focuses on studying properties of amalgamated free products $G=G_1*_{G_0} G_2$, where the amalgamated subgroup $G_0$ is virtually cyclic. First, we prove that if the factors $G_1$ and $G_2$ are finitely generated virtually…

We study a characteristic subgroup of finitely generated groups, consisting of elements with uniform upper bound for word-lengths. For a group $G$, we denote this subgroup by $G_{bound}$. We give sufficient criteria for triviality and…

We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs, admitting a certain error decomposition. This class includes randomized explicit and…

We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define…

We study word metrics on Z^d by developing tools that are fine enough to measure dependence on the generating set. We obtain counting and distribution results for the words of length n. With this, we show that counting measure on spheres…