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The spectral dimension of random trees

C. Destri·L. Donetti
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Abstract

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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C. Destri, L. Donetti. 2002-12-16. The spectral dimension of random trees. https://doi.org/10.1088/0305-4470%2F35%2F45%2F301

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