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- W4317942092 abstract "Introduced in the early days of random matrix theory, the auto-covariances $delta I^j_k={rm cov}(s_j, s_{j+k})$ of level spacings ${s_j}$ accommodate a detailed information on correlations between individual eigenlevels. It was first conjectured by F. Dyson that the auto-covariances of distant eigenlevels in the unfolded spectra of infinite-dimensional random matrices should exhibit a power-law decay $delta I^j_kapprox -1/betapi^2k^2$, where $beta$ is the symmetry index. In this paper, we establish an exact link between the auto-covariances of level spacings and their power spectrum, and show that it admits a representation in terms of a fifth Painlev'e transcendent. This result is further exploited to determine an asymptotic expansion for auto-covariances that reproduces the Dyson formula as well as provides the sub-leading corrections to it. High-precision numerical simulations lend independent support to our results." @default.
- W4317942092 created "2023-01-25" @default.
- W4317942092 creator A5040810043 @default.
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- W4317942092 date "2023-01-23" @default.
- W4317942092 modified "2023-09-23" @default.
- W4317942092 title "Power spectra and auto-covariances of level spacings beyond the Dyson conjecture" @default.
- W4317942092 doi "https://doi.org/10.48550/arxiv.2301.09441" @default.
- W4317942092 hasPublicationYear "2023" @default.
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