arXiv subjects

Maksym Chaudkhari

Publications and source records attributed to Maksym Chaudkhari.

4 recordsLinked to original sources

arXiv2026

Amenable equivalence relations, Kesten's property, and measurable lamplighters

We prove a characterization of the amenability of countable Borel equivalence relations in terms of the uniform Liouville property for group actions on their classes. Furthermore, inspired by a well-known amenability criterion for locally compact groups due to Kesten, we study return probabilities for random walks, and in particular a limiting condition that we call Kesten's property, on general topological groups. We show that every amenable topological group with small invariant neighborhoods indeed has Kesten's property. For measurable lamplighter groups associated with countable Borel equivalence relations, we establish a connection between Kesten's property and anti-concentration inequalities for the inverted orbits of random walks on the equivalence classes. This allows us to construct an amenable contractible Polish group without Kesten's property.

math.GR↗

arXiv2025

The CLT for lamplighter groups with an acylindrically hyperbolic base

We prove a Central Limit Theorem for the drift of a non-elementary random walk with a finite exponential moment on a wreath product $A\wr H=\bigoplus_{H} A\rtimes H$ with $A$ a non-trivial finite group and $H$ a finitely generated acylindrically hyperbolic group. We also provide the upper bounds on the central moments of the drift. Furthermore, our results extend to the case where $A$ is an arbitrary (possibly infinite) finitely generated group.

math.PR↗

arXiv2024

Hyperlinear approximations to amenable groups come from sofic approximations

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 probabilistic, using the concentration of measure in high-dimensional spheres to control the deviation of an operator's matrix coefficients from its trace. As a corollary, we obtain a result connecting stability of sofic approximations with stability of hyperlinear approximations.

math.GR↗

arXiv2018

Confined subgroups of Thompson's group $F$ and its embeddings into wobbling groups

We obtain a characterisation of confined subgroups of Thompson's group $F$. As a result, we deduce that orbital graph of a point under action of $F$ has uniformly subexponential growth if and only if this point is fixed by the commutator subgroup. This allows us to prove non-embeddability of $F$ into wobbling groups of graphs with uniformly subexponential growth.

math.GR↗