Density of eigenvalues of random band matrices

Abstract

Using methods of supersymmetry, we calculate the distribution of eigenvalues for random Hermitian band matrices. We show that, if the bandwidth b increases with the dimension of matrices N as b∝${\mathit{N}}^{\mathrm{\beta }}$ with some β>0, the resulting eigenvalue distribution is given by Wigner’s semicircle law as in the case of full random matrices of the Gaussian unitary ensemble.