The spectral dimension of random brushes
Statistical Mechanics
2015-06-01 v1
Abstract
We consider a class of random graphs, called random brushes, which are constructed by adding linear graphs of random lengths to the vertices of Z^d viewed as a graph. We prove that for d=2 all random brushes have spectral dimension d_s=2. For d=3 we have {5\over 2}\leq d_s\leq 3 and for d\geq 4 we have 3\leq d_s\leq d.
Keywords
Cite
@article{arxiv.0709.3678,
title = {The spectral dimension of random brushes},
author = {Thordur Jonsson and Sigurdur Orn Stefansson},
journal= {arXiv preprint arXiv:0709.3678},
year = {2015}
}
Comments
15 pages, 1 figure