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arXiv · 1312.0423

Eigenvalue distribution of large weighted bipartite random graphs

Valentin Vengerovsky
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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 $\fracα{1-α}$ and the average number of edges attached to one vertex is $α\cdot p$ or $(1-α)\cdot p$. 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.

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Valentin Vengerovsky. 2013-12-02. Eigenvalue distribution of large weighted bipartite random graphs. https://arxiv.org/abs/1312.0423

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