Statistical properties of structured random matrices
Abstract
Spectral properties of Hermitian Toeplitz, Hankel, and ToeplitzplusHankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral statistics of all these lowcomplexity random matrices is of the intermediate type, characterized by: (i) level repulsion at short distances, (ii) an exponential decrease in the nearestneighbor distributions at long distances, (iii) a nontrivial value of the spectral compressibility, and (iv) the existence of nontrivial fractal dimensions of eigenvectors in Fourier space. Our findings show that intermediatetype statistics is more ubiquitous and universal than was considered so far and open a new direction in random matrix theory.
 Publication:

Physical Review E
 Pub Date:
 April 2021
 DOI:
 10.1103/PhysRevE.103.042213
 arXiv:
 arXiv:2012.14322
 Bibcode:
 2021PhRvE.103d2213B
 Keywords:

 Mathematical Physics;
 Quantum Physics
 EPrint:
 34 pages, 7 figures