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

Autor(es)

Veneziani, Alexei M. ^[1] ; Pereira, Tiago ^[1] ; Marchetti, Domingos H. U. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Matemat Computacao & Cognicao, Santo Andre, SP - Brazil

^[2] Univ Sao Paulo, Inst Fis, BR-05315 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 53, n. 2 FEB 2012.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 02/10954-7 - Polinômios ortogonais e a estatística dos autovalores de matrizes aleatórias
• Beneficiário: Alexei Magalhães Veneziani
• Linha de fomento: Bolsas no Brasil - Doutorado Direto