Global Fluctuations of Gaussian Elliptic Matrices
Abstract
We introduce a spoke-arc decomposition of non-crossing annular pair partitions NC2(p,q) that records spoke type and orientation, isolates spoke-level contributions, and factorizes the dependence on the ellipticity parameter γ 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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