Essential spectrum and Weyl asymptotics for discrete Laplacians
Language
en
Document de travail - Pré-publication
English Abstract
In this paper, we investigate spectral properties of discrete Laplacians. Our study is based on the Hardy inequality and the use of super-harmonic functions. We recover and improve lower bounds for the bottom of the spectrum ...Read more >
In this paper, we investigate spectral properties of discrete Laplacians. Our study is based on the Hardy inequality and the use of super-harmonic functions. We recover and improve lower bounds for the bottom of the spectrum and of the essential spectrum. In some situation, we obtain Weyl asymptotics for the eigenvalues. We also provide a probabilistic representation of super-harmonic functions. Using coupling arguments, we set comparison results for the bottom of the spectrum, the bottom of the essential spectrum and the stochastic completeness of different discrete Laplacians. The class of weakly spherically symmetric graphs is also studied in full detail.Read less <
English Keywords
discrete Laplacian
locally finite graphs
asympotic of eigenvalues
spectrum
essential spectrum
markov chains
functional inequalities
Origin
Hal imported