Deviation probabilities for extremal eigenvalues of large Chiral non-Hermitian random matrices

Abstract

Abstract Consider the chiral non-Hermitian random matrix ensemble with parameters n and v, and let ( ζ i ) 1 ≤ i ≤ n {(\zeta_{i})_{1\leq i\leq n}} be its n eigenvalues with positive x-coordinate. In this paper, we establish deviation probabilities and moderate deviation probabilities for the spectral radius ( n n + v ) 1 2 ⁢ max 1 ≤ i ≤ n ⁡ | ζ i | 2 {(\frac{n}{n+v})^{\frac{1}{2}}\max_{1\leq i\leq n}|\zeta_{i}|^{2}} , as well as ( n n + v ) 1 2 ⁢ min 1 ≤ i ≤ n ⁡ | ζ i | 2 {(\frac{n}{n+v})^{\frac{1}{2}}\min_{1\leq i\leq n}|\zeta_{i}|^{2}} .