Matches in SemOpenAlex for { <https://semopenalex.org/work/W2999272200> ?p ?o ?g. }
- W2999272200 abstract "We consider the number ${mathcal{N}}_{{ensuremath{theta}}_{A}}(ensuremath{theta})$ of eigenvalues ${e}^{i{ensuremath{theta}}_{j}}$ of a random unitary matrix, drawn from ${mathrm{CUE}}_{ensuremath{beta}}(N)$, in the interval ${ensuremath{theta}}_{j}ensuremath{in}[{ensuremath{theta}}_{A},ensuremath{theta}]$. The deviations from its mean, ${mathcal{N}}_{{ensuremath{theta}}_{A}}(ensuremath{theta})ensuremath{-}mathbb{E}[{mathcal{N}}_{{ensuremath{theta}}_{A}}(ensuremath{theta})]$, form a random process as function of $ensuremath{theta}$. We study the maximum of this process, by exploiting the mapping onto the statistical mechanics of log-correlated random landscapes. By using an extended Fisher-Hartwig conjecture supplemented with the freezing duality conjecture for log-correlated fields, we obtain the cumulants of the distribution of that maximum for any $ensuremath{beta}>0$. It exhibits combined features of standard counting statistics of fermions (free for $ensuremath{beta}=2$ and with Sutherland-type interaction for $ensuremath{beta}ensuremath{ne}2$) in an interval and extremal statistics of the fractional Brownian motion with Hurst index $H=0$. The $ensuremath{beta}=2$ results are expected to apply to the statistics of zeroes of the Riemann Zeta function." @default.
- W2999272200 created "2020-01-23" @default.
- W2999272200 creator A5011588658 @default.
- W2999272200 creator A5031449563 @default.
- W2999272200 date "2020-05-27" @default.
- W2999272200 modified "2023-10-18" @default.
- W2999272200 title "Statistics of Extremes in Eigenvalue-Counting Staircases" @default.
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- W2999272200 doi "https://doi.org/10.1103/physrevlett.124.210602" @default.
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