46 citations · 150 across the 22 of their papers we have counts for
26 papers
On the ET0L subgroup membership problem in bounded automata groups
Alex Bishop, Daniele D'Angeli, Francesco Matucci +3
We are interested in the subgroup membership problem in groups acting on rooted -regular trees and a natural class of subgroups, the stabilisers of infinite rays emanating from…
Abelian Sandpiles on Cylinders
Jean-Pierre Eckmann, Tatiana Nagnibeda, Aymeric Perriard
We study here a variant of the Abelian Sandpile Model, where the playground is a cylinder of width and of circumference c. When c << w, we describe a phenomenon which has not b…
Spectral measures and dominant vertices in graphs of bounded degree
Claire Bruchez, Pierre de la Harpe, Tatiana Nagnibeda
A graph of bounded degree has an adjacency operator~ which acts on the Hilbert space . There are different kinds of measures of interest on the spectrum…
On the -colorable subgroup and maximal subgroups of Thompson's group
Valeriano Aiello, Tatiana Nagnibeda
In his work on representations of Thompson's group , Vaughan Jones defined and studied the -\emph{colorable subgroup} of . Later, Ren showed that it is isomo…
On spectra and spectral measures of Schreier and Cayley graphs
Rostislav Grigorchuk, Tatiana Nagnibeda, Aitor Pérez
We are interested in various aspects of spectral rigidity of Cayley and Schreier graphs of finitely generated groups. For each pair of integers and , we consider…
Schreier graphs of spinal groups
Tatiana Nagnibeda, Aitor Pérez
We study Schreier dynamical systems associated with a vast family of groups that hosts many known examples of groups of intermediate growth. We are interested in the orbital graphs…
On the oriented Thompson subgroup and its relatives in higher Brown-Thompson groups
Valeriano Aiello, Tatiana Nagnibeda
A few years ago the so-called oriented subgroup of the Thompson group was introduced by V. Jones while investigating the connections between subfactors and conformal f…
Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs
Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda +1
We introduce a class of subshifts governed by finitely many two-sided infinite words. We call these words leading sequences. We show that any locally constant cocycle over such a s…
Combinatorics of the subshift associated to Grigorchuk's group
Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda
We study combinatorial properties of the subshift induced by the substitution that describes Lysenok's presentation of Grigorchuk's group of intermediate growth by generators and r…
Ends of Schreier graphs and cut-points of limit spaces of self-similar groups
Ievgen Bondarenko, Daniele D'Angeli, Tatiana Nagnibeda
Every self-similar group acts on the space of infinite words over some alphabet . We study the Schreier graphs for of the action of self-similar groups ge…
Schreier graphs of Grigorchuk's group and a subshift associated to a non-primitive substitution
Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda
There is a recently discovered connection between the spectral theory of Schrö-dinger operators whose potentials exhibit aperiodic order and that of Laplacians associated with acti…
Universal groups of intermediate growth and their invariant random subgroups
Mustafa Gokhan Benli, Rostislav Grigorchuk, Tatiana Nagnibeda
We exhibit examples of groups of intermediate growth with ergodic, continuous, invariant random subgroups. The examples are the universal groups associated with a fa…
Weakly maximal subgroups in regular branch groups
Khalid Bou-Rabee, Paul-Henry Leemann, Tatiana Nagnibeda
Let be a finitely generated regular branch group acting by automorphisms on a regular rooted tree . It is well-known that stabilizers of infinite rays in (aka parabolic…
Lamplighter groups, de Bruijn graphs, spider-web graphs and their spectra
Rostislav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda
We describe the infinite family of spider-web graphs , , and , studied in physical literature as tensor products of well-known de Brujin…
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…
On transitivity and (non)amenability of Aut(F_n) actions on group presentations
Aglaia Myropolska, Tatiana Nagnibeda
For a finitely generated group the Nielsen graph , , describes the action of the group of automorphisms of the fre…
Weighted Coxeter graphs and generalized geometric representations of Coxeter Groups
Vadim Bugaenko, Yonah Cherniavsky, Tatiana Nagnibeda +1
We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient cond…
Boundaries of -free groups
Andrei Malyutin, Tatiana Nagnibeda, Denis Serbin
In this paper we study random walks on a finitely generated group which has a free action on a -tree. We show that if is non-abelian and acts minimally, freel…
Small spectral radius and percolation constants on non-amenable Cayley graphs
Kate Juschenko, Tatiana Nagnibeda
Motivated by the Benjamini-Schramm non-unicity of percolation conjecture we study the following question. For a given finitely generated non-amenable group , does there exist a…
Counting dimer coverings on self-similar Schreier graphs
Daniele D'Angeli, Alfredo Donno, Tatiana Nagnibeda
We study partition functions for the dimer model on families of finite graphs converging to infinite self-similar graphs and forming approximation sequences to certain well-known f…
Subset currents on free groups
Ilya Kapovich, Tatiana Nagnibeda
We introduce and study the space of \emph{subset currents} on the free group . A subset current on is a positive -invariant locally finite Borel measure on the spac…
Partition functions of the Ising model on some self-similar Schreier graphs
Daniele D'Angeli, Alfredo Donno, Tatiana Nagnibeda
We study partition functions and thermodynamic limits for the Ising model on three families of finite graphs converging to infinite self-similar graphs. They are provided by three…
Schreier graphs of the Basilica group
Daniele D'Angeli, Alfredo Donno, Michel Matter +1
With any self-similar action of a finitely generated group of automorphisms of a regular rooted tree can be naturally associated an infinite sequence of finite graphs $\{Γ_…
Ergodic properties of boundary actions and Nielsen--Schreier theory
Rostislav Grigorchuk, Vadim A. Kaimanovich, Tatiana Nagnibeda
We study the basic ergodic properties (ergodicity and conservativity) of the action of an arbitrary subgroup of a free group on the boundary with respect to th…