论文标题
在低温下，平面库仑气体的差异提高了
Improved discrepancy for the planar Coulomb gas at low temperatures
论文作者
论文摘要
我们研究了平面库仑气体在逆温度$β_n$的制度中至少在粒子数量$ n $的数量（冻结状态，$β_N\ gtrsim \ log n $）的情况下生长。我们表明，几乎肯定对于大$ n $，任何显微镜区域的粒子数量与其期望值（以平衡度量为准的精度给出）是对数因子的差异，这是观测窗口周围的顺序。这些估计值在整个液滴（颗粒积累的区域）中有效，并且在边界附近特别有趣，而在批量方面，它们对已知结果进行了技术改进。 我们的工作以低温在低温下等均分配的最新结果为基础，并通过为ERFC-KERNEL范围的某些Toeplitz操作员提供精制的光谱渐近学（有时称为Faddeeva或等离子体分散核心）。
We study the planar Coulomb gas in the regime where the inverse temperature $β_n$ grows at least logarithmically with respect to the number of particles $n$ (freezing regime, $β_n\gtrsim \log n$). We show that, almost surely for large $n$, the discrepancy between the number of particles in any microscopic region and their expected value (given with adequate precision by the equilibrium measure) is, up to log factors, of the order of the perimeter of the observation window. The estimates are valid throughout the whole droplet (the region where the particles accumulate), and are particularly interesting near the boundary, while in the bulk they offer technical improvements over known results. Our work builds on recent results on equidistribution at low temperatures and improves on them by providing refined spectral asymptotics for certain Toeplitz operators on the range of the erfc-kernel (sometimes called Faddeeva or plasma dispersion kernel).
