论文标题
随机零的禁止区域：正交域的出现
The forbidden region for random zeros: appearance of quadrature domains
论文作者
论文摘要
我们的主要发现是一方面正交域之间的令人惊讶的相互作用，另一方面是高斯整个功能（GEF）的零过程。具体而言，考虑在罕见的孔事件中的GEF，即给定的大约旦域中没有零。我们表明，在自然缩放限制中，封闭孔的正交结构域以零密度消失的禁区出现。此外，我们对禁止区域是磁盘的那些孔进行描述。 随机零与潜在理论之间的连接联系是由Zeitouni-Zelditch功能的极端问题提供的。为了解决这个问题，我们根据一个看似新颖的障碍物问题对其进行了重新铸造，在该问题中，该解决方案被迫在孔内部进行谐波。
Our main discovery is a surprising interplay between quadrature domains on the one hand, and the zero process of the Gaussian Entire Function (GEF) on the other. Specifically, consider the GEF conditioned on the rare hole event that there are no zeros in a given large Jordan domain. We show that in the natural scaling limit, a quadrature domain enclosing the hole emerges as a forbidden region, where the zero density vanishes. Moreover, we give a description of those holes for which the forbidden region is a disk. The connecting link between random zeros and potential theory is supplied by a constrained extremal problem for the Zeitouni-Zelditch functional. To solve this problem, we recast it in terms of a seemingly novel obstacle problem, where the solution is forced to be harmonic inside the hole.
