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The statistical geometry of scale-free random trees

Luca Donetti and Claudio Destri

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The properties of random trees (Galton–Watson trees) with scale-free (power-like) probability distribution of coordinations are investigated in the thermodynamic limit. The scaling form of volume probability is found, and the connectivity dimensions are determined and compared with other exponents which describe the growth. The (local) spectral dimension is also determined through the study of the massless limit of the Gaussian model on such trees.


PACS

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

02.10.Ox Combinatorics; graph theory

02.50.Cw Probability theory

02.40.-k Geometry, differential geometry, and topology

MSC

05C80 Random graphs

05C05 Trees

Subjects

Mathematical physics

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 23 (11 June 2004)

Received 11 December 2003

Published 25 May 2004



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