Deviation and moderate deviation for extremal eigenvalues of large Chiral non-Hermitian random matrices

Abstract

Consider the chiral non-Hermitian random matrix ensemble with parameters $n$ and $v,$ and let $(\hat{I}{\P }_i{)}_{1\le i\le n}$ be its $n$ eigenvalues with positive $x$-coordinate. In this paper, we establish deviation probabilities and moderate deviation probabilities for the spectral radius $(n/(n+v){)}^{1/2}{\max }_{1\le i\le n}|\hat{I}{\P }_i{|}^2,$ as well as $(n/(n+v){)}^{1/2}{\min }_{1\le i\le n}|\hat{I}{\P }_i{|}^2.$