English

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

R2 v1 2026-06-21T09:20:49.968Z