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The spectral dimension of random brushes

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.

preprint2007arXivOpen access
Thordur JonssonSigurdur Orn Stefansson
cond-mat.stat-mech
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Thordur JonssonSigurdur Orn Stefansson

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