Eigenphase distributions of unimodular circular ensembles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909092509908992 |
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| author | Nishigaki, Shinsuke |
| author_facet | Nishigaki, Shinsuke |
| contents | Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices ($β$=2), supported by explicit examples at small N and by numerical samplings at larger N. In this note, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric ($β$=1) and selfdual ($β$=4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenphase distributions of unimodular circular ensembles Nishigaki, Shinsuke Mathematical Physics Disordered Systems and Neural Networks High Energy Physics - Lattice High Energy Physics - Theory Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices ($β$=2), supported by explicit examples at small N and by numerical samplings at larger N. In this note, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric ($β$=1) and selfdual ($β$=4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively. |
| title | Eigenphase distributions of unimodular circular ensembles |
| topic | Mathematical Physics Disordered Systems and Neural Networks High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.09045 |