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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Veneziani, Alexei M. [1] ; Pereira, Tiago [1] ; Marchetti, Domingos H. U. [2]
Total Authors: 3
Affiliation:
[1] Univ Fed ABC, Ctr Matemat Computacao & Cognicao, Santo Andre, SP - Brazil
[2] Univ Sao Paulo, Inst Fis, BR-05315 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Mathematical Physics; v. 53, n. 2 FEB 2012.
Web of Science Citations: 2
Abstract

The method of steepest descent is used 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(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. {[}http://dx.doi.org/10.1063/1.3688293] (AU)