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## Abstract

We develop a method to compute the moments of the eigenvalue densities of matrices in the Gaussian, Laguerre, and Jacobi ensembles for all the symmetry classes β ∈ {1, 2, 4} and finite matrix dimension n. The moments of the Jacobi ensembles have a physical interpretation as the moments of the transmission eigenvalues of an electron through a quantum dot with chaotic dynamics. For the Laguerre ensemble we also evaluate the finite n negative moments. Physically, they correspond to the moments of the proper delay times, which are the eigenvalues of the Wigner-Smith matrix. Our formulae are well suited to an asymptotic analysis as n → ∞.

Translated title of the contribution | Moments of the transmission eigenvalues, proper delay times and random matrix theory |
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Original language | English |

Article number | 103511 |

Number of pages | 29 |

Journal | Journal of Mathematical Physics |

Volume | 52 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2011 |

### Bibliographical note

Publisher: American Institute of Physics## Fingerprint Dive into the research topics of 'Moments of the transmission eigenvalues, proper delay times, and random matrix theory. I'. Together they form a unique fingerprint.

## Projects

- 1 Finished