### Abstract

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices H_{N} with independent Gaussian entries such that {H_{i j} Hlk} = δ_{ik}δ _{jl} J_{ij} , where J = (−W^{2}Δ+1) ^{−1}.Assuming that W^{2} = N^{1+θ}, 0 < θ ≤ 1, we showthat themoment’s asymptotic behavior (as N → ∞) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.

Original language | English (US) |
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Pages (from-to) | 45-82 |

Number of pages | 38 |

Journal | Communications In Mathematical Physics |

Volume | 328 |

Issue number | 1 |

DOIs | |

State | Published - Mar 5 2014 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Shcherbina, T. (2014). On the second mixed moment of the characteristic polynomials of 1D band matrices.

*Communications In Mathematical Physics*,*328*(1), 45-82. https://doi.org/10.1007/s00220-014-1947-7