### Abstract

An explicit formula for the mean spectral measure of a random Jacobi matrix is derived. The matrix can be regarded as the limit of Gaussian beta ensemble (GβE) matrices as the matrix size N tends to infinity with the constraint that N β is a constant.

Original language | English |
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Article number | 68 |

Journal | Electronic Communications in Probability |

Volume | 20 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

### Keywords

- Gaussian beta ensemble
- Random jacobi matrix
- Self-convolutive recurrence
- Spectral measure

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Duy, T. K., & Shirai, T. (2015). The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles.

*Electronic Communications in Probability*,*20*, [68]. https://doi.org/10.1214/ECP.v20-4252