74 citations · 131 across the 18 of their papers we have counts for
10 papers · 1 filter
Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs
Oleksiy Khorunzhiy
We consider the ensemble of real random symmetric matrices obtained from the determinant form of the Ihara zeta function associated to random graphs $Γ_N^{(…
On eigenvalue distribution of random matrices of Ihara zeta function of large random graphs
O. Khorunzhiy
We consider the ensemble of real symmetric random matrices obtained from the determinant form of the Ihara zeta function of random graphs that have vertices with th…
On high moments of strongly diluted large Wigner random matrices
O. Khorunzhiy
We consider a dilute version of the Wigner ensemble of nxn random matrices and study the asymptotic behavior of their moments in the limit of infinite , and …
On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices
Oleksiy Khorunzhiy
We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average ρ_n non-zero elements. We study asymptotic properties of th…
On correlation function of high moments of Wigner random matrices
Oleksiy Khorunzhiy
We consider the Wigner ensemble of Hermitian n-dimensional random matrices and study the correlation function K(s',s") of their moments in the limit when the numbers s', s" of the…
Even Walks and Estimates of High Moments of Large Wigner Random Matrices
O. Khorunzhiy, V. Vengerovsky
We revisit the problem of estimates of moments of random n-dimensional matrices of Wigner ensemble by using the approach elaborated by Ya. Sinai and A. Soshnikov and further develo…
On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models
O. Khorunzhiy
Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian, we introduce two families of discrete matrix models constructed both with the help of the Erdos-Ren…
Asymptotic Behavior of Partition Functions with Graph Laplacian
Oleksiy Khorunzhiy
We introduce the matrix sums that represent a discrete analog of the matrix models with quartic potential. The probability space is given by the set of all simple n-vertex graphs w…
Estimates for moments of random matrices with Gaussian elements
O. Khorunzhiy
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic…
Lifshitz tails for spectra of Erdős--Rényi random graphs
Oleksiy Khorunzhiy, Werner Kirsch, Peter Müller
We consider the discrete Laplace operator on Erdős--Rényi random graphs with vertices and edge probability . We are interested in the limiting spectral propertie…