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

Yutao Ma; Siyu Wang

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arXiv · 2409.16755

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

Yutao Ma·Siyu Wang

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Abstract

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 $(n/(n+v))^{1/2}\max_{1\le i\le n}|\zeta_i|^2,$ as well as $(n/(n+v))^{1/2}\min_{1\le i\le n}|\zeta_i|^2.$

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Yutao Ma, Siyu Wang. 2024-09-25. Deviation and moderate deviation for extremal eigenvalues of large Chiral non-Hermitian random matrices. https://arxiv.org/abs/2409.16755

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