An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Spectral asymptotics of percolation Laplacians on amenable Cayley graphs

Author: Tonci Antunovic (Chemnitz) and Ivan Veselic (Chemnitz).

Abstract

We study spectral properties of subcritical edge-percolation subgraphs of Cayley graphs of finitely generated, amenable groups. More precisely, we consider Laplace operators which are normalised in such a way that zero is the infimum of the spectrum and analyse the asymptotic behaviour of the integrated density of states near zero.