13
IRUS Total
Downloads

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

File Description SizeFormat 
Journal of Mathematical Physics_53_2_2012.pdfAccepted version502.73 kBAdobe PDFView/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