On the spectral density function of the Laplacian of a graph
Combinatorics
2015-02-24 v2
Abstract
Let X be a finite graph. Let E be the number of its edges and d be its degree. Denote by F_1(X) its first spectral density function which counts the number of eigenvalues less or equal to lambda^2 of the associated Laplace operator. We prove the estimate F_1(X)(lambda) - F_1(X)(0) le 2 cdot E cdot d cdot lambda for 0 le lambda < 1. We explain how this gives evidence for conjectures about approximating Fuglede-Kadison determinants and L^2-torsion.
Keywords
Cite
@article{arxiv.1205.2321,
title = {On the spectral density function of the Laplacian of a graph},
author = {Herbert Koch and Wolfgang Lueck},
journal= {arXiv preprint arXiv:1205.2321},
year = {2015}
}
Comments
final version, added new references, 9 pages, to appear in Expositiones Mathematicae