2013/10/04 by E. Bogomolny, Olivier Giraud, O. Giraud
Mathematics · Physics and Astronomy · #Applied mathematics #Combinatorics #Computer science #Eigenvalues and eigenvectors #Existential quantification #Graph #Limit (mathematics) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Quantum mechanics #Random Matrices and Applications #Random graph #Random matrix #Relation (database) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.88.062811
23 pages
arxiv created 2013/10/04 · openalex publication_date 2013/12/11 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For random matrices with treelike structure there exists a recursive relation for the local Green functions whose solution permits us to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this article 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.