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arXiv · 1504.05758

Fluctuations of the eigenvalue number in the fixed interval for $\beta$-models with $\beta=1,2,4$

Mariya Shcherbina
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Abstract

We study the fluctuation of the eigenvalue number of any fixed interval $\Delta=[a,b]$ inside the spectrum for $\beta$- ensembles of random matrices in the case $\beta=1,2,4$. We assume that the potential $V$ is polynomial and consider the cases of any multi-cut support of the equilibrium measure. It is shown that fluctuations become gaussian in the limit $n\to\infty$, if they are normalized by $\pi^{-2}\log n$.

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Mariya Shcherbina. 2015-04-22. Fluctuations of the eigenvalue number in the fixed interval for $\beta$-models with $\beta=1,2,4$. https://arxiv.org/abs/1504.05758

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