Eigenvalue distribution of large weighted bipartite random graphs

2013/12/02 by Valentin Vengerovsky, Vengerovsky, Valentin
Mathematics · #Advanced Algebra and Geometry #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1312.0423

openalex publication_date 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study eigenvalue distribution of the adjacency matrix A^{(N,p, α)} of weighted random bipartite graphs Γ= Γ_N,p. We assume that the graphs have N vertices, the ratio of parts is \fracα1-α and the average number of edges attached to one vertex is α⋅ p or (1-α)⋅ p. To each edge of the graph e_ij we assign a weight given by a random variable a_ij with all moments finite. We consider the moments of normalized eigenvalue counting measure σ_{N,p, α} of A^{(N,p, α)}. The weak convergence in probability of normalized eigenvalue counting measures is proved.

Citations

• On the Distribution of the Roots of Certain Symmetric Matrices

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