论文标题
高斯随机地图进入飞机的奇异性
Singularities of Gaussian Random Maps into the Plane
论文作者
论文摘要
我们计算与N维紧凑型歧管上一对平滑中心的高斯随机场的两次平滑中心的高斯随机场相关的各种数量的预期值，例如固定指数的临界曲线和轮廓的长度和cusps的数量。除两个字段的平滑度以外，我们没有在没有特定假设的情况下获得某些表达式，但是在不同级别的其他约束下，例如两个随机字段，例如i.i.d，固定，同位素，等等。
We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on an n-dimensional compact manifold, such as the lengths of the critical curves and contours of a fixed index and the number of cusps. We obtain certain expressions under no particular assumptions other than smoothness of the two fields, but more explicit formulae are derived under varying levels of additional constraints such as the two random fields being i.i.d, stationary, isotropic etc.
