Transfer matrix approach to 1d random band matrices: density of states

Abstract

We study the special case of $n\times n$ 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix $J=(-W^2△+1{)}^{-1}$. Assuming that $n\ge CW\log W\gg 1$, we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order $W^{-1}$.

27 p

References in corpus (2)

• Universality of the local regime for the block band matrices with a finite number of blocks
• Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I

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