The idea of self-similarity is one of the most fundamental in the modern mathematics. The
notion of “renormalization group”, which plays an essential role in quantum field theory …

For a random walk on a finitely generated group G we obtain a generalization of a classical
inequality of Ancona. We deduce as a corollary that the identity map on G extends to a …

We prove that when a countable group admits a nontrivial Floyd-type boundary, then every
nonelementary and metrically proper subgroup contains a noncommutative free subgroup …

We give a proof of the sublinear tracking property for sample paths of random walks on
various groups acting on spaces with hyperbolic-like properties. As an application, we prove …

We answer positively a question of Kaimanovich and Vershik from 1979, showing that the
final configuration of lamps for simple random walk on the lamplighter group over Zd (d≥ 3) …

We introduce a curvature function for planar graphs to study the connection between the
curvature and the geometric and spectral properties of the graph. We show that non-positive …

We study isometric actions of certain groups on metric spaces with hyperbolic-type
bordifications. The class of groups considered includes SL n (ℤ), Artin braid groups and …

We introduce a natural combinatorial curvature function on the corners of plane tessellations
and relate it to the global metric geometry of their corresponding edge and dual graphs. If …

We study branching Markov chains on a countable state space (space of types) X with the
focus on the qualitative aspects of the limit behaviour of the evolving empirical population …

We are interested in the Guivarc'h inequality for admissible random walks on finitely
generated relatively hyperbolic groups, endowed with a word metric. We show that for …