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arXiv · 1106.4858

Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials

Alexei M. Veneziani·Tiago Pereira·Domingos H. U. Marchetti
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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.

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Alexei M. Veneziani, Tiago Pereira, Domingos H. U. Marchetti. 2011-06-23. Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials. https://doi.org/10.1063/1.3688293

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