Calculation of mean spectral density for statistically uniform tree-like random models

Abstract

For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this note is to investigate and compare expressions for the spectral density of random regular graphs, based on easy approximations for real solutions of the recursive relation valid for trees with large coordination number. The obtained formulas are in a good agreement with the results of numerical calculations even for small coordination number.

23 pages

References in corpus (2)

• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Lifshitz tails on the Bethe lattice: a combinatorial approach

Cited by in corpus (4)

• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Network community structure and resilience to localized damage: application to brain microcirculation
• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
• Critical properties of disordered XY model on sparse random graphs