Local laws for polynomials of Wigner matrices

Laszlo Erdos, Torben Kruger, Yuriy Nemish

Published 2018-04-30Version 1

We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have constant variance. Under some numerically checkable conditions, we establish the optimal local law, i.e., we show that the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory.