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

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