Related papers: Statistical hyperbolicity in groups

We show that the set $SA(G)$ of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic group $G$ is dense in the product of the sets $SA(P)$ over all maximal parabolic subgroups $P$. The set $BSA(G)$…

We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using…

We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…

We consider groups defined by cyclic presentations where the defining word has length three and the cyclic presentation satisfies the T(6) small cancellation condition. We classify when these groups are hyperbolic. When combined with known…

A recently fertile strand of research in Group Theory is developing non-abelian analogues of classical combinatorial results for arithmetic Cayley graphs, describing properties such as growth, expansion, mixing, diameter, etc. We consider…

We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to contruct a boundary for a group that is an acylindrical amalgamation of relatively…

We study a class of two dimensional partially hyperbolic systems, not necessarily skew products, trying to establish the germ of a general theory. To illustrate the scope of the theory, we apply our results to the case of fast-slow…

In 1996, Gersten proved that finitely presented subgroups of a word hyperbolic group of integral cohomological dimension 2 are hyperbolic. We use isoperimetric inequalities over arbitrary rings to extend this result to any ring. In…

We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we…

We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically…

We investigate a coarse version of a $2(n+1)$-point inequality characterizing metric spaces of combinatorial dimension at most $n$ due to Dress. This condition, experimentally called $(n,\delta)$-hyperbolicity, reduces to Gromov's quadruple…

This article studies the properties of word-hyperbolic semigroups and monoids, i.e. those having context-free multiplication tables with respect to a regular combing, as defined by Duncan & Gilman. In particular, the preservation of…

We study the girth of Cayley graphs of finite classical groups G on random sets of generators. Our main tool is an essentially best possible bound we obtain on the probability that a given word w takes the value 1 when evaluated in G in…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

We introduce the notion of finite stature of a family $\{H_i\}$ of subgroups of a group $G$. We investigate the separability of subgroups of a group $G$ that splits as a graph of hyperbolic special groups with quasiconvex edge groups. We…

We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either…

In this paper, we construct a family of asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to -6. The manifolds we constructed can be arbitrary close to anti-de Sitter-Schwarzschild manifolds at infinity.…

Let $\Gamma$ be a nonelementary hyperbolic group with a word metric $d$ and $\partial\Gamma$ its hyperbolic boundary equipped with a visual metric $d_a$ for some parameter $a>1$. Fix a superexponential symmetric probability $\mu$ on…

We construct Patterson-Sullivan measure and a natural metric on the unit space of a hyperbolic groupoid. In particular, this gives a new approach to defining SRB measures on Smale spaces using Gromov hyperbolic graphs.