43 citations · 93 across the 21 of their papers we have counts for
17 papers · 1 filter
Finite dimensional amenable groups
Anna Erschler, Ivan Mitrofanov
We show that an amenable group of finite Assouad-Nagata dimension satisfies the property of Shalom. Such infinite groups are known to admit a virtual homomorphism onto $\m…
Poisson Boundary for Upper-Triangular Groups
Anna Erschler, Josh Frisch, Mark Rychnovsky
We prove that finite entropy random walks on the torsion-free Baumslag group in dimension have non-trivial Poisson boundary. This is in contrast with the torsion case where t…
Poisson boundary of group extensions
Anna Erschler, Joshua Frisch
Given a finitely generated group, the well-known Stability Problem asks whether the non-triviality of the Poisson-Furstenberg boundary (which is equivalent to the existence of non-…
Assouad-Nagata dimension and gap for ordered metric spaces
Anna Erschler, Ivan Mitrofanov
We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true.…
Arboreal structures on groups and the associated boundaries
Anna Erschler, Vadim Kaimanovich
For any countable group with infinite conjugacy classes we construct a family of forests on the group. For each of them there is a random walk on the group with the property that i…
Growth of periodic Grigorchuk groups
Anna Erschler, Tianyi Zheng
On torsion Grigorchuk groups we construct random walks of finite entropy and power-law tail decay with non-trivial Poisson boundary. Such random walks provide near optimal volume l…
No iterated identities satisfied by all finite groups
Anna Erschler, Alexei Kanel-Belov
We show that there is no iterated identity satisfied by all finite groups. For being a non-trivial word of length , we show that there exists a finite group of cardinali…
Isoperimetric inequalities, shapes of Følner sets and groups with Shalom's property
Anna Erschler, Tianyi Zheng
We prove an isoperimetric inequality for groups. As an application, we obtain lower bound on Følner functions in various nilpotent-by-cyclic groups. Under a regularity assumption,…
Almost invariance of distributions for random walks on groups
Anna Erschler
We study the neighborhoods of a typical point visited at -th step of a random walk, determined by the condition that the transition probabilities stay close to $μ^{*n}(Z_n…
Iterated identities and iterational depth of groups
Anna Erschler
Given word on letters, we study groups which satisfiy "iterated identity" , meaning that for all there exists such that -the iteration of of Eng…
Distortion of imbeddings of groups of intermediate growth into metric spaces
Laurent Bartholdi, Anna G. Erschler
For every metric space in which there exists a sequence of finite groups of bounded-size generating set that does not embed coarsely, and for every unbounded, increasi…
Imbeddings into groups of intermediate growth
Laurent Bartholdi, Anna Erschler
Every countable group that does not contain a finitely generated subgroup of exponential growth imbeds in a finitely generated group of subexponential growth. This produces in part…
Ordering the space of finitely generated groups
Laurent Bartholdi, Anna Erschler
We consider the oriented graph whose vertices are isomorphism classes of finitely generated groups, with an edge from G to H if, for some generating set T in H and some sequence of…
Groups of given intermediate word growth
Laurent Bartholdi, Anna Erschler
We show that there exists a finitely generated group of growth ~f for all functions f:\mathbb{R}\rightarrow\mathbb{R} satisfying f(2R) \leq f(R)^{2} \leq f(ηR) for all R large enou…
Poisson-Furstenberg boundary and growth of groups
Laurent Bartholdi, Anna G. Erschler
We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first…
Growth of permutational extensions
Laurent Bartholdi, Anna G. Erschler
We study the geometry of a class of group extensions, containing permutational wreath products, which we call "permutational extensions". We construct for all natural number k a to…
Fundamental groups of asymptotic cones
A. G. Erschler, D. V. Osin
We show that for any metric space satisfying certain natural conditions, there is a finitely generated group , an ultrafilter , and an isometric embedding of to t…