Geodesic
On eigenvalue distribution of random matrices of Ihara zeta function of large random graphs
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 3, pp. 268-282 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the ensemble of real symmetric random matrices $H^{(n,\rho)}$ obtained from the determinant form of the Ihara zeta function of random graphs that have $n$ vertices with the edge probability $\rho/n$. We prove that the normalized eigenvalue counting function of $H^{(n,\rho)}$ converges weakly in average as $n,\rho\to\infty$ and $\rho=o(n^\alpha)$ for any $\alpha>0$ to a shift of the Wigner semi-circle distribution. Our results support a conjecture that the large Erdős–Rényi random graphs satisfy in average the weak graph theory Riemann Hypothesis. 
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O. Khorunzhiy. On eigenvalue distribution of random matrices of Ihara zeta function of large random graphs. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 3, pp. 268-282. http://geodesic.mathdoc.fr/item/JMAG_2017_13_3_a3/

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