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.
"The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles." Electron. Commun. Probab. 20 1 - 13, 2015. https://doi.org/10.1214/ECP.v20-4252