论文标题
面孔随机大超晶状体
Faces in random great hypersphere tessellations
论文作者
论文摘要
引入并研究了典型和加权典型的球形面孔，用于$ n $ n $独立的随机随机大型超球产生的$ d $维单元球体的镶嵌面孔。给出了此类球面的概率解释，并确定其方向分布。在各向同性的情况下，可在预期的$ f $ - vector，预期的球形Quermaßintegrals和预期的球形内在体积的明确公式。讨论了它们作为$ n \ to \ infty $的限制行为，并将其与欧几里得案中的相应概念和结果进行了比较。研究了预期的统计维度和与球形随机多型相交概率有关的问题。
The concept of typical and weighted typical spherical faces for tessellations of the $d$-dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed according to a non-degenerate directional distribution, is introduced and studied. Probabilistic interpretations for such spherical faces are given and their directional distributions are determined. Explicit formulas for the expected $f$-vector, the expected spherical Quermaßintegrals and the expected spherical intrinsic volumes are found in the isotropic case. Their limiting behaviour as $n\to\infty$ is discussed and compared to the corresponding notions and results in the Euclidean case. The expected statistical dimension and a problem related to intersection probabilities of spherical random polytopes is investigated.
