Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials
Mathematical Physics
2015-05-28 v1 math.MP
Probability
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^{-N\Sigma_{i=1}^{N}V_{\alpha}(z_{i})} \Pi_{1\leqi<j\leqN}|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.
Cite
@article{arxiv.1106.4858,
title = {Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials},
author = {Alexei M. Veneziani and Tiago Pereira and Domingos H. U. Marchetti},
journal= {arXiv preprint arXiv:1106.4858},
year = {2015}
}
Comments
25 pages, 2 figures