论文标题
局部排斥平面高斯关键点
Local repulsion of planar Gaussian critical points
论文作者
论文摘要
我们研究固定各向同性平滑平面高斯田的临界点之间的局部排斥。我们表明，关键点可以体验到一个软排斥，这在随机平面波模型的情况下是最大的，或者是任意高阶的软吸引力。如果指定了临界点的类型（极端，马鞍点），则这些点会经历局部排斥，我们可以用小球中第二个阶乘数量的确切量化量化。
We study the local repulsion between critical points of a stationary isotropic smooth planar Gaussian field. We show that the critical points can experience a soft repulsion which is maximal in the case of the random planar wave model, or a soft attraction of arbitrary high order. If the type of critical points is specified (extremum, saddle point), the points experience a hard local repulsion, that we quantify with the precise magnitude of the second factorial moment of the number of points in a small ball.
