论文标题
在真实的吉尼伯合奏中稀薄的真实特征值的边缘分布
Edge distribution of thinned real eigenvalues in the real Ginibre ensemble
论文作者
论文摘要
本文涉及对实际ginibre集合中最大的真实特征值的限制分布函数的明确计算，当每个真实特征值都以恒定的可能性独立删除时。我们表明，\ cite {bb}中最近发现的可集成结构从真实的ginibre合奏中概括到其稀薄的等效物。具体而言，我们将上述限制分布函数表达为两个简单的弗雷德姆决定因素的凸组合，并将相同的函数连接到Zakharov-Shabat系统的反散射理论。作为推论，我们提供了Zakharov-Shabat评估整体的真实特征值生成功能，并获得对限制分布函数的尾巴的精确控制。后一部分包括通常恒定因子的明确计算。
This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed independently with constant likelihood. We show that the recently discovered integrable structures in \cite{BB} generalize from the real Ginibre ensemble to its thinned equivalent. Concretely, we express the aforementioned limiting distribution function as a convex combination of two simple Fredholm determinants and connect the same function to the inverse scattering theory of the Zakharov-Shabat system. As corollaries, we provide a Zakharov-Shabat evaluation of the ensemble's real eigenvalue generating function and obtain precise control over the limiting distribution function's tails. The latter part includes the explicit computation of the usually difficult constant factors.
