The spectral dimension of random brushes

Details The spectral dimension of random brushes The spectral dimension of random brushes

2007-09-24

arxiv.org/abs/0709.3678v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 1 figure

Scientific paper

10.1088/1751-8113/41/4/045005

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.

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