论文标题
弱非热性的复杂椭圆形的集合：边间距分布
The complex elliptic Ginibre ensemble at weak non-Hermiticity: edge spacing distributions
论文作者
论文摘要
本文的重点是在弱非热性极限的复杂椭圆形集合中最右的特征值的分布函数。我们展示了如何以全图差的parelevé-II函数来表达限制分布函数，以及相同的poisson和airy点过程之间的非平凡过渡的极端价值统计量会降低，而相同的分布函数如何捕获泊松和通风点过程之间的非平凡过渡。我们最明确的新结果涉及限制分布功能的尾巴渐近学。对于右尾，我们根据非热性程度统一地计算出领先的渐进级，对于左尾，我们将其计算到寄生虫附近。
The focus of this paper is on the distribution function of the rightmost eigenvalue for the complex elliptic Ginibre ensemble in the limit of weak non-Hermiticity. We show how the limiting distribution function can be expressed in terms of an integro-differential Painlevé-II function and how the same captures the non-trivial transition between Poisson and Airy point process extreme value statistics as the degree of non-Hermiticity decreases. Our most explicit new results concern the tail asymptotics of the limiting distribution function. For the right tail we compute the leading order asymptotics uniformly in the degree of non-Hermiticity, for the left tail we compute it close to Hermiticity.
