László Erdős

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math.PR2024

Cusp Universality for Correlated Random Matrices

László Erdős, Joscha Henheik, Volodymyr Riabov

For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states…

math.PR2024

Optimal decay of eigenvector overlap for non-Hermitian random matrices

Giorgio Cipolloni, László Erdős, Yuanyuan Xu

We consider the standard overlap $O_{ij} := ⟨ r_{j}, r_{i} ⟩ ⟨ l_{j}, l_{i} ⟩$ of any bi-orthogonal family of left and rig…

math.PR2024

Non-Hermitian spectral universality at critical points

Giorgio Cipolloni, László Erdős, Hong Chang Ji

For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$ , we prove that the local eigenvalue statistics of $A + X$ close to the critical edge poi…