关于微分同胚变换下高斯随机场的临界点
On critical points of Gaussian random fields under diffeomorphic transformations.
作者信息
Cheng Dan, Schwartzman Armin
机构信息
Arizona State University.
University of California, San Diego.
出版信息
Stat Probab Lett. 2020 Mar;158. doi: 10.1016/j.spl.2019.108672. Epub 2019 Nov 14.
Abstract
Let and be smooth Gaussian random fields parameterized on Riemannian manifolds and , respectively, such that , where is a diffeomorphic transformation. We study the expected number and height distribution of the critical points of in connection with those of . As an important case, when is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field , while the height distribution remains the same as that of .
摘要
设(X)和(Y)分别是在黎曼流形(M)和(N)上参数化的光滑高斯随机场，使得(Y = X\circ\varphi)，其中(\varphi)是一个微分同胚变换。我们研究(Y)的临界点的期望数量和高度分布，并将其与(X)的临界点的期望数量和高度分布相关联。作为一个重要的情况，当(X)是一个各向异性高斯随机场时，我们证明其临界点的期望数量与一个各向同性场(Z)的临界点的期望数量成比例，而高度分布与(Z)的高度分布保持相同。
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