### Abstract

We consider the deformed Gaussian Ensemble H_{n} = H_{n}^{(0)}+M_{n} in which H_{n}^{(0)} is a hermitian matrix (possibly random) and M_{n} is the Gaussian Unitary Ensemble (GUE) random matrix (independent of H_{n}^{(0)}). Assuming that the Normalized Counting Measure of H_{n}^{(0)} converges weakly (in probability) to a nonrandom measure N ^{(0)} with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of H_{n}.

Original language | English (US) |
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Pages (from-to) | 396-433 |

Number of pages | 38 |

Journal | Journal of Mathematical Physics, Analysis, Geometry |

Volume | 5 |

Issue number | 4 |

State | Published - 2009 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### Keywords

- Gaussian unitary ensemble
- Random matrices
- Universality

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## Cite this

Shcherbina, T. (2009). On universality of bulk local regime of the deformed Gaussian unitary ensemble.

*Journal of Mathematical Physics, Analysis, Geometry*,*5*(4), 396-433.