The spectral dimension of random trees

Details The spectral dimension of random trees The spectral dimension of random trees

2002-06-13

arxiv.org/abs/cond-mat/0206233v2

J.Phys.A35:9499-9516,2002

Physics

Condensed Matter

14 pages, 2 eps figures, revtex4. Revised version: changes in section IV

Scientific paper

10.1088/0305-4470/35/45/301

We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favor of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.

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