Determinants of Random Unitary Pencils
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908394229596160 |
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| author | Jury, Michael T. Roman, George |
| author_facet | Jury, Michael T. Roman, George |
| contents | We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by integrating against the Haar measure on the unitary group. We obtain an exact formula in the case of scalar coefficients, and conjecture an asymptotic formula in the general case, and prove a special case of the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determinants of Random Unitary Pencils Jury, Michael T. Roman, George Functional Analysis Mathematical Physics 15A52, 15A15, 46L54, 46E22 We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by integrating against the Haar measure on the unitary group. We obtain an exact formula in the case of scalar coefficients, and conjecture an asymptotic formula in the general case, and prove a special case of the conjecture. |
| title | Determinants of Random Unitary Pencils |
| topic | Functional Analysis Mathematical Physics 15A52, 15A15, 46L54, 46E22 |
| url | https://arxiv.org/abs/2506.04400 |