AI 中文总结
该研究分析中间 regime 随机单纯复形的拓扑，证明其具高度连通性与迭代悬挂同伦型，提出更灵活的高连通性组合判据，确定其拓扑复杂度上界为2且齐次类几乎必然等于2。
AI 中文摘要
我们分析中间 regime 下随机单纯复形的拓扑，证明这些复形具有高度连通性且同伦型为迭代悬挂。我们的主要工具之一是一种新的单纯复形高连通性组合判据，它比锥性更灵活。我们还证明，中间 regime 随机单纯复形的拓扑复杂度上界为2，且对于一类齐次中间 regime 随机单纯复形，该复杂度几乎必然等于2。
英文摘要
We analyse topology of random simplicial complexes in the medial regime. We show that these complexes are highly connected and have homotopy type of iterated suspensions. One of our main tools is a new combinatorial criterion for high connectivity of simplicial complexes, which is more flexible than conicity. We show that topological complexity of random simplical complexes in the medial regime is bounded above by 2 and it equals 2 for a class of homogenous medial regime random simplicial complexes, a.a.s.
Comments18 pages
