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- W2933256814 abstract "We study the Ginibre ensemble of $N times N$ complex random matrices and compute exactly, for any finite $N$, the full distribution as well as all the cumulants of the number $N_r$ of eigenvalues within a disk of radius $r$ centered at the origin. In the limit of large $N$, when the average density of eigenvalues becomes uniform over the unit disk, we show that for $0<r<1$ the fluctuations of $N_r$ around its mean value $langle N_r rangle approx N r^2$ display three different regimes: (i) a typical Gaussian regime where the fluctuations are of order ${cal O}(N^{1/4})$, (ii) an intermediate regime where $N_r - langle N_r rangle = {cal O}(sqrt{N})$, and (iii) a large deviation regime where $N_r - langle N_r rangle = {cal O}({N})$. This intermediate behaviour (ii) had been overlooked in previous studies and we show here that it ensures a smooth matching between the typical and the large deviation regimes. In addition, we demonstrate that this intermediate regime controls all the (centred) cumulants of $N_r$, which are all of order ${cal O}(sqrt{N})$, and we compute them explicitly. Our analytical results are corroborated by precise importance sampling Monte Carlo simulations." @default.
- W2933256814 created "2019-04-11" @default.
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- W2933256814 date "2019-07-25" @default.
- W2933256814 modified "2023-10-10" @default.
- W2933256814 title "Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble" @default.
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- W2933256814 doi "https://doi.org/10.1103/physreve.100.012137" @default.
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