Statistical properties of structured random matrices

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical analytic arguments it is demonstrated that spectral statistics all these intermediate type, characterized by (i) level repulsion at small distances, (ii) an exponential decrease the nearest-neighbor distributions large (iii) a non-trivial value compressibility, (iv) existence fractal dimensions eigenvectors in Fourier space. Our findings show intermediate-type more ubiquitous universal than was considered so far open new direction matrix theory.