论文标题
关于高斯随机字段临界点数量的第二刻的有限性
On the finiteness of the second moment of the number of critical points of Gaussian random fields
论文作者
论文摘要
我们证明，任何足够规则的随机场的临界点数量的第二刻，例如，在紧凑的惠特尼分层歧管上定义的几乎$ c^3 $样本路径是有限的。我们的结果无需假设平稳性 - 传统上是在其他工作中假定的。在平稳性下，我们证明了我们实施的条件意味着Estrade 2016的普遍条件。
We prove that the second moment of the number of critical points of any sufficiently regular random field, for example with almost surely $ C^3 $ sample paths, defined over a compact Whitney stratified manifold is finite. Our results hold without the assumption of stationarity - which has traditionally been assumed in other work. Under stationarity we demonstrate that our imposed conditions imply the generalized Geman condition of Estrade 2016.
