The main topic of the book is amenable groups, ie, groups on which there exist invariant
finitely additive measures. It was discovered that the existence or non-existence of …

We show that the amenability of a group acting by homeomorphisms can be deduced from a
certain local property of the action and recurrency of the orbital Schreier graphs. This applies …

Extensive amenability is a property of group actions which has recently been used as a tool
to prove amenability of groups. We study this property and prove that it is preserved under a …

We prove that every linear-activity automaton group is amenable. The proof is based on
showing that a random walk on a specially constructed degree 1 automaton group–the …

Speed Exponents of Random Walks on Groups | International Mathematics Research
Notices | Oxford Academic Skip to Main Content Advertisement Oxford Academic Journals …

A variety of behaviors of entropy functions of random walks on finitely generated groups is
presented, showing that for any 12≦α≦β\leq1, there is a group Γ with measure μ …

We show that on groups generated by bounded activity automata, every symmetric, finitely
supported probability measure has the Liouville property. More generally we show this for …

The present paper investigates the limit $ G $-space $\mathcal {J} _ {G} $ generated by the
self-similar action of automatic groups on a regular rooted tree. The limit space $\mathcal {J} …

Conformal dimension is a fundamental invariant of metric spaces, particularly suited to the
study of self-similar spaces, such as spaces with an expanding self-covering (eg Julia sets of …

We study the isoperimetric and spectral profiles of certain families of finitely generated
groups defined via actions on labelled Schreier graphs and simple gluing of such. In one of …