Upper tail large deviations for extremal eigenvalues of the real, complex and symplectic elliptic Ginibre matrices
Year: 2026
Type: preprint
Abstract: We consider the elliptic Ginibre ensembles in the real, complex and symplectic symmetry classes. As the matrix size tends to infinity, we derive the asymptotic behaviour of the upper tail large deviation probabilities for both the spectral radius and the rightmost eigenvalue. More generally, we obtain asymptotic formulas for the probability that an eigenvalue is found in a prescribed region outside the support of the elliptic law, thereby providing a unified framework in which the results for the spectral radius and the rightmost eigenvalue appear as special cases. The key ingredient of our analysis is the precise asymptotic behaviour of the associated one-point functions, which is of independent interest.
Source: arXiv (Cornell University)
Authors: Byun, Sung-Soo, Lee, Yong-Woo, Oh, Seungjoon
Institution: Seoul National University
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7138956819
Cites:
Cited by:
Related to: