### Abstract

The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for H = A + V, where A is the base matrix and V is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of eigenvalues of H in an interval, and present tail bounds for the distribution of the Frobenius and operator norms of H^{-1} and for the distribution of the norm of H^{-1} applied to a fixed vector. The bounds are uniform in A and exceed the actual suprema by no more than multiplicative constants. The probability of multiple eigenvalues in an interval is also estimated.

Original language | English (US) |
---|---|

Article number | 1750028 |

Journal | Communications in Contemporary Mathematics |

Volume | 19 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Keywords

- Gaussian perturbation
- Minami estimate
- Wegner estimate
- deformed GOE
- deformed GUE

## Fingerprint Dive into the research topics of 'Matrix regularizing effects of Gaussian perturbations'. Together they form a unique fingerprint.

## Cite this

Aizenman, M., Peled, R., Schenker, J., Shamis, M., & Sodin, S. (2017). Matrix regularizing effects of Gaussian perturbations.

*Communications in Contemporary Mathematics*,*19*(3), [1750028]. https://doi.org/10.1142/S0219199717500286