AI 中文总结
本文基于RDT重新确认Kronecker-Gaussian矩阵的Lehner公式，有效重新证明了经典高斯随机系综的强渐近自由性关键结果。
AI 中文摘要
已有显著突破[25,43]确立了经典高斯随机系综与其半圆自由对应物之间的强渐近自由性。与之类似，与自由对应物相关的Lehner公式[31]精确确定了Kronecker-Gaussian矩阵的谱边缘。本文不利用随机矩阵理论和谱方法，重新审视并研究该公式，尤其依赖随机对偶理论（Random Duality Theory, RDT）[45,46,51]中的概念，重新确认Lehner公式，并有效重新证明了[25,43]中通过谱方法得到的关键渐近自由性结果。
英文摘要
Remarkable breakthroughs [25,43] established the so-called strong asymptotic freeness between classical Gaussian random ensembles and their semicircular free counterparts. Along the same lines, the Lehner formula [31], associated with the free counterpart, precisely determines the spectral edges of Kronecker-Gaussian matrices. We here revisit and study this formula without the utilization of random matrix theory and spectral methods. In particular, relying on concepts utilized within \emph{Random Duality Theory} (RDT) [45,46,51], we reconfirm Lehner's formula and effectively reprove the key asymptotic freeness results obtained via spectral methods in [25,43].
