Open AccessRandom Gromov’s monsters do not act non-elementarily on hyperbolic spaces
Author(s) -
Dominik Gruber,
Alessandro Sisto,
Romain Tessera
Publication year - 2020
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14754
Subject(s) - monster , mathematics , geodesic , hyperbolic group , relatively hyperbolic group , random walk , pure mathematics , combinatorics , discrete mathematics , hyperbolic manifold , mathematical analysis , hyperbolic function , statistics , physics , quantum mechanics
We show that Gromov’s monster groups arising from i.i.d. labelings of expander graphs do not admit non-elementary actions on geodesic hyperbolic spaces. The proof relies on comparing properties of random walks on randomly labeled graphs and on groups acting non-elementarily on hyperbolic spaces.