The spectral dimension of random brushes
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 Zd viewed as a graph. We prove that for d=2 all random brushes have spectral dimension ds=2. For d=3 we have 5 2≤ ds≤ 3 and for d≥ 4 we have 3≤ ds≤ d.
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