论文标题
高斯宗旨，高斯决定因素和高斯随机场
Gaussian Zonoids, Gaussian determinants and Gaussian random fields
论文作者
论文摘要
我们研究与非中心高斯载体相关的Vitale Zonoid（与概率分布相关的凸形体）。这定义了一个凸体的家族，其中包含并概括了椭圆形，我们称之为高斯层。我们表明，每个高斯派层都可以通过我们明确计算的椭圆形近似。我们使用此结果来给出新的估计值，以预期非中心高斯基质的绝对值根据椭圆形的混合体积。最后，利用Stecconi和作者发现的随机场与Zonoids之间的最新联系，我们将结果应用于零中心的高斯随机场的研究。我们展示了如何通过合适的中心高斯随机场近似这些，并在方差为零的情况下给出定量渐近线。
We study the Vitale zonoid (a convex body associated to a probability distribution) associated to a non--centered Gaussian vector. This defines a family of convex bodies, that contains and generalizes ellipsoids, which we call Gaussian zonoids. We show that each Gaussian zonoid can be approximated by an ellipsoid that we compute explicitely. We use this result to give new estimates for the expectation of the absolute value of the determinant of a non--centered Gaussian matrix in terms of mixed volume of ellipsoids. Finally, exploiting a recent link between random fields and zonoids uncovered by Stecconi and the author, we apply our results to the study of the zero set of non--centered Gaussian random fields. We show how these can be approximated by a suitable centered Gaussian random field and give a quantitative asymptotic in the limit where the variance goes to zero.
