Electronic Communications in Probability

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

Khanh Trinh Duy and Tomoyuki Shirai

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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.

Article information

Electron. Commun. Probab., Volume 20 (2015), paper no. 68, 13 pp.

Accepted: 26 September 2015
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B80: Random operators [See also 47H40, 60H25]

random Jacobi matrix Gaussian beta ensemble spectral measure self-convolutive recurrence

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Duy, Khanh Trinh; Shirai, Tomoyuki. The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles. Electron. Commun. Probab. 20 (2015), paper no. 68, 13 pp. doi:10.1214/ECP.v20-4252. https://projecteuclid.org/euclid.ecp/1465320995

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