高斯随机矩阵积和式根的旋转半圆律
Rotated semicircle laws for permanental roots of Gaussian random matrices
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中文总结 AI 辅助
本研究针对标准GOE与GUE矩阵，证明其积和式特征多项式的归一化零点计数测度几乎必然收敛于旋转π/2后的Wigner半圆律，验证了Fyodorov提出的相关猜想。
中文摘要 AI 辅助
针对取自标准高斯正交系综（GOE）和高斯酉系综（GUE）的矩阵，我们证明了积和式特征多项式$Per(zI_N-H_N)$的归一化零点计数测度几乎必然收敛于$[-2,2]$上的标准Wigner半圆律，该半圆律经$\pi/2$旋转后落在虚轴上。这证明了Fyodorov在文献[Fyodorov2006]中提出的猜想。
英文摘要
For matrices drawn from the standard Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE), we prove that the normalized zero counting measure of the permanental characteristic polynomial $Per(zI_N-H_N)$ converges almost surely to the standard Wigner semicircle law on $[-2,2]$, rotated by $π/2$ onto the imaginary axis. This proves the conjecture proposed by Fyodorov in \cite{Fyodorov2006}.
