Asymptotic integral kernel for ensembles of random normal matrices with radial potentials
- Veneziani, AM
- Pereira, T
- Marchetti, DHU
Publication date
January 2012
DOI Publisher
AIP Publishing ISSN
0022-2488 Journal
Journal of Mathematical Physics Language
English Citation count (estimate)
3Abstract
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
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