On the Gaussian measure of the intersection of symmetric, convex sets

Limit laws for functionals of self-intersection symmetric alpha-stable processes

In this paper, we prove two limit laws for functionals of self-intersection symmetric alpha-stable processes with alpha\in(1,2). The results are obtained based on the method of moments, the sample configuration and the chaining argument introduced in (Nualart and Xu 2013) are employed.

Sampling by Intersections with Random Geodesics

In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from zero, the observed length will deviate from the actual measure by at most a fixed error for any subset, while in convex bodies we can always choose a subset for which the behavior would be close to a zero-one law, as the dimension grows. The result for the sphere is based on an analysis of the Radon transform. Using similar tools we analyze the variance of …

Conditionally Evenly Convex Sets and Evenly Quasi-Convex Maps

Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem. This notion is then applied to obtain the dual representation of conditionally evenly quasi-convex maps.

Gaussian Correlation Conjecture for Symmetric Convex Sets

Gaussian correlation conjecture states that the Gaussian measure of the intersection of two symmetric convex sets is greater or equal to the product of the measures.

凸集的高斯近似：通过半空间交集

Gaussian Approximation of Convex Sets by Intersections of Halfspaces

本文系统研究高斯分布下凸集用半空间交集的近似复杂度，证明原点中心高斯体积1/2的ℓ2球需且仅需2^Θ(√n)个半空间，ℓp球(1≤p<2)需2^Õ(n^{3/4})个，并利用多领域技术建立上下界。

The Gaussian Correlation Inequality for Symmetric Convex Sets

The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures. Characterization of the equality and some applications are given.