129 citations · 401 across the 50 of their papers we have counts for
6 papers · 2 filters
Ergodic decomposition of group actions on rooted trees
Rostislav Grigorchuk, Dmytro Savchuk
We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of erg…
Spectra of Schreier graphs of Grigorchuk's group and Schroedinger operators with aperiodic order
Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda
We study spectral properties of the Laplacians on Schreier graphs arising from Grigorchuk's group acting on the boundary of the infinite binary tree. We establish a connection betw…
Self-similar groups, automatic sequences, and unitriangular representations
R. Grigorchuk, Y. Leonov, V. Nekrashevych +1
We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matric…
On the condensation property of the Lamplighter groups and groups of Intermediate growth
Mustafa Gokhan Benli, Rostislav Grigorchuk
The aim of this short note is to revisit some old results about groups of intermediate growth and groups of the lamplighter type and to show that the Lamplighter group $L=\mathbb{Z…
Amenability and ergodic properties of topological groups: from Bogolyubov onwards
Rostislav Grigorchuk, Pierre de la Harpe
The purpose of this expository article is to revisit the notions of amenability and ergodicity, and to point out that they appear for topological groups that are not necessarily lo…
Characteristic random subgroups of geometric groups and free abelian groups of infinite rank
Lewis Bowen, Rostislav Grigorchuk, Rostyslav Kravchenko
We show that if is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then has $…