发表机构
Peking University（北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究秩一尖峰复Ginibre系综在非厄米BBP相变处的最大特征值实部，证明亚临界尖峰不影响Gumbel极限并给出收敛速率修正，临界点建立上界。
AI 中文摘要
我们研究一个秩一的尖峰复Ginibre系综 A_N = X_N + sigma u u^*，其中 X_N 是一个 N×N 复Ginibre矩阵，其独立元素服从 CN(0,1/N) 分布，u 是一个确定性单位向量，sigma 是非负尖峰强度。我们关注特征值实部的最大值及其在非厄米BBP相变附近的行为。对于每个固定的亚临界尖峰强度 sigma < 1，我们证明在相同的中心化和缩放后，最大实部与无尖峰系综具有相同的Gumbel极限。我们还推导了无尖峰Gumbel律的显式收敛速率修正，其阶为 1/log N。在临界点 sigma = 1，我们利用各向同性预解估计和网格论证，在 N^{-1/4} 尺度上建立了最右特征值的上界。
英文摘要
We study a rank-one spiked complex Ginibre ensemble A_N = X_N + sigma u u^*, where X_N is an N by N complex Ginibre matrix with independent entries distributed as CN(0,1/N), u is a deterministic unit vector, and sigma is a nonnegative spike strength. We focus on the maximum real part of the eigenvalues and its behavior near the non-Hermitian BBP transition. For every fixed subcritical spike strength sigma < 1, we show that the maximum real part has the same Gumbel limit as in the unspiked ensemble, after the same centering and scaling. We also derive an explicit convergence-rate correction of order 1/log N for the unspiked Gumbel law. At the critical point sigma = 1, we establish an upper bound for the rightmost eigenvalue at the N^{-1/4} scale using isotropic resolvent estimates and a net argument.
Comments22 pages, 1 author, no figures. Mathematics and probability; preprint
