On the asymptotic duality of spectral variances in random matrix theory and the "1/6" formula
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911604589723648 |
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| author | Tian, Peng Riser, Roman Kanzieper, Eugene |
| author_facet | Tian, Peng Riser, Roman Kanzieper, Eugene |
| contents | A "mysterious" relation between the number variance and the variance of the $L$-th ordered eigenvalue, first suggested by French et al. [Ann. Phys. 113, 277 (1978)], is revisited and proven to be asymptotically exact for the $β=2$ Dyson symmetry class. Central to the proof is a previously unknown sum rule for the level spacing auto-covariances. Its derivation hinges on our previous work on the power spectrum description of eigenvalue fluctuations in random matrix theory. Analytical results for $β=2$ are complemented by conjectural extensions to the $β=1$ and $β=4$ symmetry classes. Our findings are corroborated by a comprehensive numerical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17150 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the asymptotic duality of spectral variances in random matrix theory and the "1/6" formula Tian, Peng Riser, Roman Kanzieper, Eugene Mathematical Physics Disordered Systems and Neural Networks High Energy Physics - Theory A "mysterious" relation between the number variance and the variance of the $L$-th ordered eigenvalue, first suggested by French et al. [Ann. Phys. 113, 277 (1978)], is revisited and proven to be asymptotically exact for the $β=2$ Dyson symmetry class. Central to the proof is a previously unknown sum rule for the level spacing auto-covariances. Its derivation hinges on our previous work on the power spectrum description of eigenvalue fluctuations in random matrix theory. Analytical results for $β=2$ are complemented by conjectural extensions to the $β=1$ and $β=4$ symmetry classes. Our findings are corroborated by a comprehensive numerical analysis. |
| title | On the asymptotic duality of spectral variances in random matrix theory and the "1/6" formula |
| topic | Mathematical Physics Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.17150 |