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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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