Eugene Bogomolny ((Paris-Saclay))

Spectral statistics of low-complexity matrices

Abstract: It is demonstrated that spectral statistics of random Toeplitz, Hankel, and Toeplitz-plus-Hakel matrices are of intermediate type typical for pseudo-integrable billiards. Wigner-type approximate formulas are obtained for these matrices in a good argreement with numerical calculations. It is observed that eigenfunctions for such matrices are multi-fractals in the Fourier space.