### Abstract

We consider ensembles of N×N Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density function of the entries, we show that the expectation of the density of states on arbitrarily small intervals converges to the semicircle law, as N tends to infinity.

Original language | English |
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Pages (from-to) | 2797-2836 |

Number of pages | 40 |

Journal | Advances in Mathematics |

Volume | 228 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Dec 2011 |

### Keywords

- Wignerʼs semicircle law;

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## Cite this

Maltsev, A. V., & Schlein, B. (2011). Average density of states for Hermitian Wigner matrices.

*Advances in Mathematics*,*228*(5), 2797-2836. https://doi.org/10.1016/j.aim.2011.06.040