Geodesic
Eigenvalue Distribution of a Large Weighted Bipartite Random Graph
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014) no. 2, pp. 240-255 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study an eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$ of the weighted random bipartite graph $\Gamma= \Gamma_{N,p}$. We assume that the graph has $N$ vertices, the ratio of parts is $\displaystyle\frac{\alpha}{1-\alpha}$, and the average number of the edges attached to one vertex is $\alpha p$ or $(1-\alpha) p$. To every edge of the graph $e_{ij}$, we assign the weight given by a random variable $a_{ij}$ with all moments finite. We consider the moments of the normalized eigenvalue counting measure $\sigma_{N,p, \alpha}$ of $A^{(N,p, \alpha)}$. The weak convergence in probability of the normalized eigenvalue counting measures is proved. 
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V. Vengerovsky. Eigenvalue Distribution of a Large Weighted Bipartite Random Graph. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014) no. 2, pp. 240-255. http://geodesic.mathdoc.fr/item/JMAG_2014_10_2_a4/

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