论文标题
Bernoulli随机配额复合物的Betti数字期望的单程性
Unimodality of the Expectation of Betti Numbers for Bernoulli Random Quota Complexes
论文作者
论文摘要
我们研究某些称为随机配额复合物的随机简单复合物。如果顶点的权重低于给定的配额，$ q $，则通过添加$ n $ simplex来构建$ n+1 $加权顶点的配额复合物。在本文中，选择了顶点的权重。带有伯努利分布。本文的主要结果是，$ m^{\ textrm {th}} $ betti编号的期望，即，$ m^{\ textrm {th}} $同源群的尺寸是$ m $中的单模式。
We study certain random simplicial complexes, called random quota complexes. A quota complex on $N+1$ weighted vertices is constructed by adding an $n$-simplex if the sum of the weights of the vertices is below a given quota, $q$. In this paper, the weights of the vertices are chosen i.i.d. with a Bernoulli distribution. The main result of this paper is that the expectation of the $m^{\textrm{th}}$ Betti number, i.e., the dimension of the $m^{\textrm{th}}$ homology group, is unimodal in $m$.
