2014/06/20 by Bonnefont, Michel, Sylvain Golénia, Golenia, Sylvain · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1406.5391
openalex publication_date 2014/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.