The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles
classification
🧮 math.SP
math.PR
keywords
betamatrixgaussianjacobimatricesmeanrandomspectral
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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.
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