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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.17150 |
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Table of 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.