We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Assuming that n≥ CWlog W≫ 1 , we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order W- 1.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Band matrices
- Density of states
- Transfer matrix approach