Related papers: Contracting elements and random walks

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently…

We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of…

We consider discrete random dynamical systems induced by a non-elementary group action on a non-proper hyperbolic space. We prove that if the system is ergodic and satisfies the ``asymptotic past and future independence condition'' as…

In this note we study the limiting behaviour of real valued functions on hyperbolic groups as we travel along typical geodesic rays in the Gromov boundary of the group. Our results apply to group homomorphisms, certain quasimorphisms and to…

We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.

In this short note, we prove the existence of weakly malnormal, virtually free, quasiconvex subgroups in any nonelementary hyperbolic group. This extends a result of Ilya Kapovich, where he proved the existence of malnormal quasiconvex…

We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of vertices $n$, as first established in recent work with…

We analyse the intersection of positively and negatively sectional-hyperbolic sets for flows on compact manifolds. First we prove that such an intersection is hyperbolic if the intersecting sets are both transitive (this is false without…

We are interested in the Guivarc'h inequality for admissible random walks on finitely generated relatively hyperbolic groups, endowed with a word metric. We show that for random walks with finite super-exponential moment, if this inequality…

In this paper, we prove that for subgroups acting on admissible multiarc and curve graphs and for the handlebody group acting on the disk graph, the loxodromic elements are exactly those for which some pure power is a pseudo-Anosov on a…

A subset $A$ of an abelian group $G$ is sequenceable if there is an ordering $(a_1, \ldots, a_k)$ of its elements such that the partial sums $(s_0, s_1, \ldots, s_k)$, given by $s_0 = 0$ and $s_i = \sum_{j=1}^i a_i$ for $1 \leq i \leq k$,…

We study two actions of big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. The first two…

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a…

Given a finite generating set $S$, let us endow the mapping class group of a closed hyperbolic surface with the word metric for $S$. We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of…

We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the…

In this paper we study hyperbolic groups acting on CAT(0) cube complexes. The first main result (Theorem A) is a structural result about the Sageev construction, in which we relate quasi-convexity of hyperplane stabilizers with…

We make a few observations on the absence of geometric and topological rigidity for acylindrically hyperbolic and relatively hyperbolic groups. In particular, we demonstrate the lack of a well-defined limit set for acylindrical actions on…

We construct new families of quasimorphisms on many groups acting on CAT(0) cube complexes. These quasimorphisms have a uniformly bounded defect of 12, and they "see" all elements that act hyperbolically on the cube complex. We deduce that…

Let G be a finitely generated group and Cay(G, S) be the Cayley graph of G with respect to a finite generating set S. We characterize the Gromov hyperbolicity of G in terms of the genericity of contracting elements in Cay(G, S).