论文标题
由sublinear期望随机向量产生的凸体
Convex bodies generated by sublinear expectations of random vectors
论文作者
论文摘要
我们表明，凸几何形状（尤其是质心体，凸面浮动物体和ULAM浮动体）中的许多众所周知的转换是一般结构的特殊实例，依赖于将sublinear期望应用于欧几里得空间中的随机载体。我们确定了此类凸形体的双重表示，并描述了一种构造，该结构是所有如此定义的凸体的组成部分。
We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random vectors in Euclidean space. We identify the dual representation of such convex bodies and describe a construction that serves as a building block for all so defined convex bodies.
