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arXiv · 1605.05206

Mesoscopic central limit theorem for general $β$-ensembles

Florent Bekerman·Asad Lodhia
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Abstract

We prove that the linear statistics of eigenvalues of $β$-log gasses satisfying the one-cut and off-critical assumption with a potential $V \in C^6(\mathbb{R})$ satisfy a central limit theorem at all mesoscopic scales $α\in (0; 1)$. We prove this for compactly supported test functions $f \in C^5(\mathbb{R})$ using loop equations at all orders along with rigidity estimates.

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Florent Bekerman, Asad Lodhia. 2016-05-17. Mesoscopic central limit theorem for general $β$-ensembles. https://arxiv.org/abs/1605.05206

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