The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles

Abstract

An explicit formula for the mean spectral measure of a random Jacobi matrix is derived. The matrix may be regarded as the limit of Gaussian beta ensemble (G$\beta$E) matrices as the matrix size $N$ tends to infinity with the constraint that $N\beta$ is a constant.

References in corpus (1)

• Moments of the Gaussian $\beta$ Ensembles and the large-$N$ expansion of the densities

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