论文标题
确定性大型链接中的单纯链接
Simplex links in determinantal hypertrees
论文作者
论文摘要
我们推断出与卡莱（Kalai）著名的枚举结果相关的确定性概率措施的结构归纳描述，用于$ n-1 $ - 单纯的较高维度的跨度树。结果，我们得出了这样的随机树中单纯链接的边际分布。在此过程中，我们还根据基本的简单复合物的高维根林来表征其他所有简单锥的较高维度的跨越树。我们还将这些新结果应用于随机拓扑，随机图的光谱分析以及高维扩展器的理论。这些结果中的一个特别有趣的推论是，$ O（\ log n）$ cestional 2-trees的基本组具有很高的可能性。
We deduce a structurally inductive description of the determinantal probability measure associated with Kalai's celebrated enumeration result for higher--dimensional spanning trees of the $n-1$--simplex. As a consequence, we derive the marginal distributions of the simplex links in such random trees. Along the way, we also characterize the higher--dimensional spanning trees of every other simplicial cone in terms of the higher--dimensional rooted forests of the underlying simplicial complex. We also apply these new results to random topology, the spectral analysis of random graphs, and the theory of high dimensional expanders. One particularly interesting corollary of these results is that the fundamental group of a union of $o(\log n)$ determinantal 2--trees has Kazhdan's property (T) with high probability.
