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- Title
Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs.
- Authors
Khorunzhiy, O.
- Abstract
We consider the ensemble of N×N real random symmetric matrices HN(R) obtained from the determinant form of the Ihara zeta function associated to random graphs ΓN(R) of the long-range percolation radius model with the edge probability determined by a function ϕ(t). We show that the normalized eigenvalue counting function of HN(R) weakly converges in average as N,R→∞, R=o(N) to a unique measure that depends on the limiting average vertex degree of ΓN(R) given by ϕ1=∫ϕ(t)dt. This measure converges in the limit of infinite ϕ1 to a shift of the Wigner semi-circle distribution. We discuss relations of these results with the properties of the Ihara zeta function and weak versions of the graph theory Riemann Hypothesis.
- Subjects
EIGENVALUES; EIGENVALUE equations; RANDOM matrices; PERCOLATION; GRAPH theory; RIEMANN hypothesis; MATHEMATICAL models
- Publication
Random Matrices: Theory & Application, 2018, Vol 7, Issue 3, pN.PAG
- ISSN
2010-3263
- Publication type
Article
- DOI
10.1142/S2010326318500077