The spectral dimension of random trees

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.

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

References in corpus (1)

• On the growth of bounded trees

Cited by in corpus (12)

• Cosmology of the Lifshitz universe
• Geometry and field theory in multi-fractional spacetime
• Multifractional theories: an unconventional review
• The spectral dimension of generic trees
• Random walks on combs
• Networks with many structural scales: a Renormalization Group perspective
• Multi-scale Laplacian community detection in heterogeneous networks
• The statistical geometry of scale-free random trees
• In an Attempt to Introduce Long-range Interactions into Small-world Networks
• Target annihilation by diffusing particles in inhomogeneous geometries
• Deterministic simplicial complexes
• Spectral densities of scale-free networks