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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320995

Digital Object Identifier
doi:10.1214/ECP.v20-4252

Mathematical Reviews number (MathSciNet)
MR3407212

Zentralblatt MATH identifier
1329.47038

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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References

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