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The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles. (English) Zbl 1329.47038
Summary: 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.

MSC:
47B80 Random linear operators
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
15B52 Random matrices (algebraic aspects)
44A60 Moment problems
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