Year: 2024
Type: preprint
Abstract: Consider a random matrix of size $N$ as an additive deformation of the complex Ginibre ensemble under a deterministic matrix $X_0$ with a finite rank, independent of $N$. We prove that microscopic statistics for the mean diagonal overlap, near the edge point, are characterized by the iterative erfc integrals, which only depend on the geometric multiplicity of certain eigenvalue of $X_0$. We also investigate the microscopic statistics for the mean diagonal overlap of the outlier eigenvalues. Further we get a phenomenon of the phase transition for the mean diagonal overlap, with respect to the modulus of the eigenvalues of $X_0$.
Source: arXiv (Cornell University)
Author: Zhang, Lu
Institution: University of Science and Technology of China
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4122547602
OpenAlex ID: W4400667995