Spectral comparison results for Laplacians on discrete graphs
Spectral Theory
2025-01-07 v2 Mathematical Physics
math.MP
Abstract
In the recent literature, various authors have studied spectral comparison results for Schr\"odinger operators with discrete spectrum in different settings including Euclidean domains and quantum graphs. In this note we derive such spectral comparison results in a rather general framework for general and possibly infinite discrete graphs. Along the way, we establish a discrete version of the local Weyl law whose proof does neither involve any Tauberian theorem nor the Weyl law as used in the continuous case.
Cite
@article{arxiv.2412.15937,
title = {Spectral comparison results for Laplacians on discrete graphs},
author = {Patrizio Bifulco and Joachim Kerner and Christian Rose},
journal= {arXiv preprint arXiv:2412.15937},
year = {2025}
}