## Abstract

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N × N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard "supersymmetry" approach, we integrate out Grassmann variables at the early stage and circumvent the use of the Hubbard-Stratonovich transformation in the "bosonic" sector. The method, suggested recently by J.V. Fyodorov [Nucl. Phys. B 621 [PM] (2002) 643], is shown to be capable of calculation when reinforced with a generalisation of the Itzykson-Zuber integral to a non-compact integration manifold. We arrive to such a generalisation by discussing the Duistermaat-Heckman localisation principle for integrals over non-compact homogeneous Kähler manifolds. In the limit of large-N the asymptotic expression for the correlation function reproduces the result outlined earlier by A.V. Andreev and B.D. Simons [Phys. Rev. Lett. 75 (1995) 2304].

Original language | American English |
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Pages (from-to) | 453-491 |

Number of pages | 39 |

Journal | Nuclear Physics B |

Volume | 630 |

Issue number | 3 |

DOIs | |

State | Published - 20 May 2002 |

Externally published | Yes |

### Bibliographical note

Funding Information:This research was supported by EPSRC grant GR/13838/01 “Random matrices close to unitary or Hermitian”.