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arXiv · 2608.26038

Rotated semicircle laws for permanental roots of Gaussian random matrices

Renjie Feng·Dong Yao
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Abstract

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 $\pi/2$ onto the imaginary axis. This proves the conjecture proposed by Fyodorov in \cite{Fyodorov2006}.

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Renjie Feng, Dong Yao. 2026-08-26. Rotated semicircle laws for permanental roots of Gaussian random matrices. https://arxiv.org/abs/2608.26038

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