Global Fluctuations of Gaussian Elliptic Matrices

Lingxuan Wu; Zhi Yin

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arXiv · 2511.20007

Global Fluctuations of Gaussian Elliptic Matrices

Lingxuan Wu·Zhi Yin

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Abstract

We introduce a spoke-arc decomposition of non-crossing annular pair partitions $NC_2(p,q)$ that records spoke type and orientation, isolates spoke-level contributions, and factorizes the dependence on the ellipticity parameter $\gamma$ into a spoke factor and arc weights. This yields closed-form descriptions of the limiting covariance of Gaussian elliptic matrices. As a corollary, we show that an independent family of Gaussian elliptic random matrices is asymptotically second-order free.

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Lingxuan Wu, Zhi Yin. 2025-11-25. Global Fluctuations of Gaussian Elliptic Matrices. https://arxiv.org/abs/2511.20007

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