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- W1857223720 endingPage "043306" @default.
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- W1857223720 abstract "For a large $ntimes m$ Gaussian matrix, we compute the joint statistics, including large deviation tails, of generalized and total variance - the scaled log-determinant $H$ and trace $T$ of the corresponding $ntimes n$ covariance matrix. Using a Coulomb gas technique, we find that the Laplace transform of their joint distribution $mathcal{P}_n(h,t)$ decays for large $n,m$ (with $c=m/ngeq 1$ fixed) as $hat{mathcal{P}}_n(s,w)approx expleft(-beta n^2 J(s,w)right)$, where $beta$ is the Dyson index of the ensemble and $J(s,w)$ is a $beta$-independent large deviation function, which we compute exactly for any $c$. The corresponding large deviation functions in real space are worked out and checked with extensive numerical simulations. The results are complemented with a finite $n,m$ treatment based on the Laguerre-Selberg integral. The statistics of atypically small log-determinants is shown to be driven by the split-off of the smallest eigenvalue, leading to an abrupt change in the large deviation speed." @default.
- W1857223720 created "2016-06-24" @default.
- W1857223720 creator A5029474578 @default.
- W1857223720 creator A5090073084 @default.
- W1857223720 date "2016-04-28" @default.
- W1857223720 modified "2023-10-16" @default.
- W1857223720 title "Large deviations of spread measures for Gaussian matrices" @default.
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- W1857223720 doi "https://doi.org/10.1088/1742-5468/2016/04/043306" @default.
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