Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case

@article{ErdHos2020CuspUF,
  title={Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case},
  author={L'aszl'o ErdHos and T. Kruger and Dominik Schr{\"o}der},
  journal={Commun Math Phys},
  year={2020},
  volume={378}
}
For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the… Expand

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