Global Fluctuations of Gaussian Elliptic Matrices
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917120690880512 |
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| author | Wu, Lingxuan Yin, Zhi |
| author_facet | Wu, Lingxuan Yin, Zhi |
| contents | 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 $γ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Fluctuations of Gaussian Elliptic Matrices Wu, Lingxuan Yin, Zhi Probability Combinatorics 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 $γ$ 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. |
| title | Global Fluctuations of Gaussian Elliptic Matrices |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2511.20007 |