Spectral properties of structured random matrices

Abstract: Motivated by the problem of metal-insulator transition in the Anderson model of condensed matter physics, I will discuss some spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries. Spectral statistics of all these random matrices turns out to be of intermediate type, as found for instance at the metal-insulator transition, or in certain pseudo-integrable billiards. Namely, nearest-neighbor spacing distributions are characterized by level repulsion at small distances and an exponential decrease at large distances, while the spectral compressibility has a non-trivial value. Such statistics are usually associated with multifractal eigenstates, and I will show that it is also the case here.

statistical mechanicsmathematical physicsprobability

Audience: researchers in the topic

Séminaire MEGA

Series comments: Description: Monthly seminar on random matrices and random graphs