AI 中文总结
该研究针对临界BBP regime下带有限秩尖峰的经典高斯随机矩阵子式最大特征值，证明其收敛到含Airy$_\beta$点过程的多尺度交错粒子系统，并将结果扩展至$\beta>0$的非经典情况
AI 中文摘要
我们考虑经典高斯随机矩阵在临界BBP regime下，具有有限秩尖峰的子式的最大特征值，证明其收敛到多尺度交错粒子系统，最低层级为Airy$_\beta$点过程，该构造与标度极限可自然扩展至非经典$\beta>0$的情况
英文摘要
We consider the largest eigenvalues of minors of the classical Gaussian random matrices with a finite rank spike in the critical BBP regime. We show that they converge to a multi-level interlacing particle system whose lowest level is the Airy$_β$ point process. Our construction and scaling limits extend in a natural way to non-classical $β>0$.
