### Abstract

We consider the block band matrices, i.e. the Hermitian matrices H_{N},N={pipe}Λ{pipe}W with elements H_{jk,αβ} where j,k ∈ Λ =[1,m]^{d} ∩ ℤ^{d} (they parameterize the lattice sites) and α β = 1,...., W(they parameterize the orbitals on each site). The entries H_{jk,α β} are random Gaussian variables with mean zero such that 〈 H_{j1k1,α1β1},H_{j2k2,α2β2}〉 =δ_{j1k2}δ_{j2k1}δ_{α1β2}δ_{β1α2}J_{j1k1} where J=1/W+α Δ /W, α < 1/4d. This matrices are the special case of Wegner's W-orbital models. Assuming that the number of sites {pipe}Λ{pipe} is finite, we prove universality of the local eigenvalue statistics of H_{N} for the energies {pipe}λ_{0}{pipe}< √2.

Original language | English (US) |
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Pages (from-to) | 466-499 |

Number of pages | 34 |

Journal | Journal of Statistical Physics |

Volume | 155 |

Issue number | 3 |

DOIs | |

State | Published - May 2014 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- Band matrices
- Random matrices
- Universality
- Wegner model

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## Cite this

Shcherbina, T. (2014). Universality of the Local Regime for the Block Band Matrices with a Finite Number of Blocks.

*Journal of Statistical Physics*,*155*(3), 466-499. https://doi.org/10.1007/s10955-014-0964-4