---
abstract: 'We considered $N\times N$ Wishart ensembles in the class $W_\mathbb{C}\left(\Sigma_N,M\right)$ (complex Wishart matrices with $M$ degrees of freedom and covariance matrix $\Sigma_N$) such that $N_0$ eigenvalues of $\Sigma_N$ is 1 and $N_1=N-N_0$ of them are $a$. We studied the limit as $M$, $N$, $N_0$ and $N_1$ all go to infinity such that $\frac{N}{M}\rightarrow c$, $\frac{N_1}{N}\rightarrow\beta$ and $0<c,\beta<1$. In this case, the limiting eigenvalue density can either be supported on 1 or 2 disjoint intervals in $\mathbb{R}_+$. In the previous paper [@Mo], we studied the universality in the case when the limiting eigenvalue density is supported on 2 intervals and in this paper, we continue the analysis and study the case when the support consists of a single interval. By using Riemann-Hilbert analysis, we have shown that under proper rescaling of the eigenvalues, the limiting correlation kernel is given by the sine kernel and the Airy kernel in the bulk and the edge of the spectrum respectively. As a consequence, the behavior of the largest eigenvalue in this model is described by the Tracy-Widom distribution.'
author:
- 'M. Y. Mo'
title: 'Universality in Complex Wishart ensembles: The 1 cut case'
---

Introduction
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Let $X$ be an $M\times N$ 