Lower bounds for the spectral radii of adjacency operators on Baumslag-Solitar groups

TL;DR

This paper employs free probability methods to establish lower bounds on the spectral radii of adjacency operators for Cayley graphs of certain non-amenable Baumslag-Solitar groups, advancing understanding of their spectral properties.

Contribution

It introduces a novel application of free probability techniques to derive spectral radius bounds for adjacency operators on Baumslag-Solitar groups.

Findings

Lower bounds for spectral radii are obtained using free probability.

The results apply to Cayley graphs of specific non-amenable Baumslag-Solitar groups.

The approach provides new insights into the spectral properties of these groups.

Abstract

We will use free probability techniques to find lower bounds for the spectral radii of the adjacency operators on the Caley graphs of some non-amenable Baumslag-Solitar groups with the standard generators.