Large Complex Correlated Wishart Matrices: The Pearcey Kernel and Expansion at the Hard Edge

@article{Hachem2015LargeCC,
  title={Large Complex Correlated Wishart Matrices: The Pearcey Kernel and Expansion at the Hard Edge},
  author={Walid Hachem and Adrien Hardy and Jamal Najim},
  journal={Electronic Journal of Probability},
  year={2015},
  volume={21},
  pages={1-36}
}
We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well. More precisely, under mild assumptions for the population covariance matrix, we show that the limiting density vanishes at generic cusp points like a cube root, and that the local eigenvalue behaviour is described by means of the Pearcey kernel if an extra decay assumption… 
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