当前位置:
X-MOL 学术
›
Random Struct. Algorithms
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
Phase transition for the volume of high‐dimensional random polytopes
Random Structures and Algorithms ( IF 0.9 ) Pub Date : 2020-12-28 , DOI: 10.1002/rsa.20986 Gilles Bonnet 1 , Zakhar Kabluchko 2 , Nicola Turchi 3
Random Structures and Algorithms ( IF 0.9 ) Pub Date : 2020-12-28 , DOI: 10.1002/rsa.20986 Gilles Bonnet 1 , Zakhar Kabluchko 2 , Nicola Turchi 3
Affiliation
The beta polytope is the convex hull of n i.i.d. random points distributed in the unit ball of according to a density proportional to if (in particular, corresponds to the uniform distribution in the ball), or uniformly on the unit sphere if . We show that the expected normalized volumes of high‐dimensional beta polytopes exhibit a phase transition and we describe its shape. We derive analogous results for the intrinsic volumes of beta polytopes and, when , their number of vertices.
中文翻译:
高维随机多态性的体积的相变
所述β-多面体是凸包Ñ IID分布在单位球上的随机点根据密度成比例,如果(特别是,对应于球的均匀分布),或均匀地在单位球面上如果。我们表明,预期的高维β多表位归一化体积显示出相变,并描述了其形状。我们得出β多表位的内在体积及其顶点数的相似结果。
更新日期:2020-12-28
中文翻译:
高维随机多态性的体积的相变
所述β-多面体是凸包Ñ IID分布在单位球上的随机点根据密度成比例,如果(特别是,对应于球的均匀分布),或均匀地在单位球面上如果。我们表明,预期的高维β多表位归一化体积显示出相变,并描述了其形状。我们得出β多表位的内在体积及其顶点数的相似结果。