论文标题
磁盘计数不变的确定过程统计的精确偏差
Precise deviations for disk counting statistics of invariant determinantal processes
论文作者
论文摘要
我们考虑二维确定过程，这些过程是旋转不变的，并研究了磁盘中点数的波动。基于Mod-Phi收敛的理论，我们获得了这些统计数据的浆果 - 埃斯恩以及精确的中度至大偏差估计值。这些结果与物理文献中的库仑气体启发式一致。当磁盘的半径$ r $ r $在不同的方向下增长时，我们还获得了随机过程$（\＃d_r）_ {r> 0} $的功能限制定理。我们向不变的确定过程提出了几种应用，包括多芯片分析的集合，高斯分析功能和其他双曲模型。作为推论，我们计算了（整数）Laughlin的纠缠熵的精确渐近剂，以供所有Landau级别。
We consider two-dimensional determinantal processes which are rotation-invariant and study the fluctuations of the number of points in disks. Based on the theory of mod-phi convergence, we obtain Berry-Esseen as well as precise moderate to large deviation estimates for these statistics. These results are consistent with the Coulomb gas heuristic from the physics literature. We also obtain functional limit theorems for the stochastic process $(\# D_r)_{r>0}$ when the radius $r$ of the disk $D_r$ is growing in different regimes. We present several applications to invariant determinantal process, including the polyanalytic Ginibre ensembles, Gaussian analytic function and other hyperbolic models. As a corollary, we compute the precise asymptotics for the entanglement entropy of (integer) Laughlin states for all Landau levels.
