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Statistical properties of structured random matrices
Eugene Bogomolny, Olivier Giraud
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical a…
Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
E. Bogomolny, M. Sieber
The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments re…
Quantum Ising model in transverse and longitudinal fields: chaotic wave functions
Y. Y. Atas, E. Bogomolny
The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of…
The distribution of the ratio of consecutive level spacings in random matrix ensembles
Y. Y. Atas, E. Bogomolny, O. Giraud +1
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was re…