Zobrazeno 1 - 10
of 202
pro vyhledávání: '"Juschenko A"'
Autor:
Bondarenko, Ievgen, Juschenko, Kate
The zero divisor conjecture is sufficient to prove for certain class of finitely presented groups where the relations are given by a pairing of generators. We associate Mealy automata to such pairings, and prove that the zero divisor conjecture holds
Externí odkaz:
http://arxiv.org/abs/2402.08625
We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a group is simulated by a suitable sofic approximation. The proof is pro
Externí odkaz:
http://arxiv.org/abs/2311.09202
We establish results connecting the uniform Liouville property of group actions on the classes of a countable Borel equivalence relation with amenability of this equivalence relation. We also study extensions of Kesten's theorem to certain classes of
Externí odkaz:
http://arxiv.org/abs/2212.00348
Publikováno v:
Comment. Math. Helv. 96 (2021) 805-851
We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in the sense of Bourbaki. We prove characterizations of skew-amenability for topological gr
Externí odkaz:
http://arxiv.org/abs/2012.09504
Autor:
Burton, Peter, Juschenko, Kate
This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite
Externí odkaz:
http://arxiv.org/abs/2003.04535
Autor:
Burton, Peter, Juschenko, Kate
In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators. We prove that this conjecture implies Connes' embedding conjecture.
Externí odkaz:
http://arxiv.org/abs/1912.12365
Autor:
Juschenko, Kate
Liouville property of actions of discrete groups can be reformulated in terms of existence co-F$\o$lner sets. Since every action of amenable group is Liouville, the property can be served as an approach for proving non-amenability. The verification o
Externí odkaz:
http://arxiv.org/abs/1806.02753
There are several natural families of groups acting on rooted trees for which every member is known to be amenable. It is, however, unclear what the elementary amenable members of these families look like. Towards clarifying this situation, we here s
Externí odkaz:
http://arxiv.org/abs/1712.08418
A subset $S$ of a group $G$ invariably generates $G$ if $G= \langle s^{g(s)} | s \in S\rangle$ for every choice of $g(s) \in G,s \in S$. We say that a group $G$ is invariably generated if such $S$ exists, or equivalently if $S=G$ invariably generates
Externí odkaz:
http://arxiv.org/abs/1611.08264
Autor:
Juschenko, Kate, Zheng, Tianyi
We provide equivalent conditions for Liouville property of actions of groups. As an application, we show that there is a Liouville measure for the action of the Thompson group $F$ on dyadic rationals. This result should be compared with a recent resu
Externí odkaz:
http://arxiv.org/abs/1608.03554