The spectral edge of some random band matrices

Abstract

We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the band is sufficiently wide (W » N 5/6). Otherwise, a different limiting distribution appears. © 2010 by Princeton University (Mathematics Department).