In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian β Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on β.

中文翻译：

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经典 beta 集成中的均匀点方差界限

在本文中，我们给出了圆形和高斯的点数方差的界限β集合成单位圆的弧或实线的间隔。这些界限相对于这些集合的重整化长度是对数的，预计在乘法常数之前是最优的，仅取决于β.