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 by-product, we obtain evidence in favour of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favour of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.
Destri, C., Donetti, L. (2002). The spectral dimension of random trees. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 35(45), 9499-9515 [10.1088/0305-4470/35/45/301].
The spectral dimension of random trees
DESTRI, CLAUDIO;
2002
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 by-product, we obtain evidence in favour of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favour of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.
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