The Manhattan curve, ergodic theory of topological flows and rigidity
S Cantrell, R Tanaka - arXiv preprint arXiv:2104.13451, 2021 - arxiv.org
For every non-elementary hyperbolic group, we introduce the Manhattan curve associated to
any pair of left-invariant hyperbolic metrics which are quasi-isometric to a word metric. It is …
any pair of left-invariant hyperbolic metrics which are quasi-isometric to a word metric. It is …
Pseudo-Anosovs are exponentially generic in mapping class groups
I Choi - arXiv preprint arXiv:2110.06678, 2021 - arxiv.org
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 …
hyperbolic surface with the word metric for $ S $. We discuss the following question: does …
Contact graphs, boundaries, and a central limit theorem for CAT (0) cubical complexes.
T Fernós, J Lécureux, F Mathéus - Groups, Geometry & Dynamics, 2024 - ems.press
Let X be a nonelementary CAT. 0/cubical complex. We prove that if X is essential and
irreducible, then the contact graph of X (introduced by Hagen (2014)) is unbounded and its …
irreducible, then the contact graph of X (introduced by Hagen (2014)) is unbounded and its …
Random walks on mapping class groups
This survey is concerned with random walks on mapping class groups. We illustrate how the
actions of mapping class groups on Teichmüller spaces or curve complexes reveal the …
actions of mapping class groups on Teichmüller spaces or curve complexes reveal the …
Central limit theorems for Green metrics on hyperbolic groups
S Cantrell, M Pollicott - arXiv preprint arXiv:2404.11512, 2024 - arxiv.org
Recently, the first author and Tanaka obtained a large deviation principle comparing two
Green metrics on a non-elementary hyperbolic group $\Gamma $ associated to finitely …
Green metrics on a non-elementary hyperbolic group $\Gamma $ associated to finitely …
Property (T) in random quotients of hyperbolic groups at densities above 1/3
CJ Ashcroft - arXiv preprint arXiv:2202.12318, 2022 - arxiv.org
We study random quotients of a fixed non-elementary hyperbolic group in the Gromov
density model. Let $ G=\langle S\;\vert\; T\rangle $ be a finite presentation of a non …
density model. Let $ G=\langle S\;\vert\; T\rangle $ be a finite presentation of a non …
Pseudo-Anosovs are exponentially generic in mapping class groups
I Choi - Geometry & Topology, 2024 - msp.org
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 …
surface with the word metric for S. We discuss the following question: does the proportion of …
Counting and boundary limit theorems for representations of Gromov‐hyperbolic groups
S Cantrell, C Sert - Proceedings of the London Mathematical …, 2023 - Wiley Online Library
Given a Gromov‐hyperbolic group GG endowed with a finite symmetric generating set, we
study the statistics of counting measures on the spheres of the associated Cayley graph …
study the statistics of counting measures on the spheres of the associated Cayley graph …
Random walks on mapping class groups
This survey is concerned with random walks on mapping class groups. We illustrate how the
actions of mapping class groups on Teichm\" uller spaces or curve complexes reveal the …
actions of mapping class groups on Teichm\" uller spaces or curve complexes reveal the …