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### Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

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Journal of Mathematical Physics_53_2_2012.pdf | Accepted version | 502.73 kB | Adobe PDF | View/Open |

Title: | Asymptotic integral kernel for ensembles of random normal matrices with radial potentials |

Authors: | Veneziani, AM Pereira, T Marchetti, DHU |

Item Type: | Journal Article |

Abstract: | We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-NSigma_{i=1}^{N}V_{alpha}(z_{i})} Pi_{1leqi<jleqN}|z_{i}-z_{j}|^{2} where V_{alpha}(z)=|z|^{alpha}, z in C and alpha in ]0,infty[. Asymptotic analysis with error estimates are obtained. A corollary of this expansion is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal--Bargmann space. |

Issue Date: | 31-Jan-2012 |

URI: | http://hdl.handle.net/10044/1/18720 |

DOI: | http://dx.doi.org/10.1063/1.3688293 |

ISSN: | 0022-2488 |

Publisher: | American Institute of Physics |

Journal / Book Title: | Journal of Mathematical Physics |

Volume: | 53 |

Issue: | 2 |

Copyright Statement: | Copyright © 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Math. Phys. 53, 023303 (2012) and may be found at http://scitation.aip.org/content/aip/journal/jmp/53/2/10.1063/1.3688293 |

Appears in Collections: | Applied Mathematics and Mathematical Physics |