Integral Homology of Random Simplicial Complexes

被引：17
作者：
Auczak, Tomasz [1 ]
Peled, Yuval [2 ]
机构：
[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, Umultowska 87, PL-61614 Poznan, Poland
[2] Givat Ram Hebrew Univ, Sch Comp Sci & Engn Edmond Safra Campus, IL-91904 Jerusalem, Israel
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2018年 / 59卷 / 01期
关键词：
Random simplicial complexes; Hitting time; Homology Shadow; CONNECTIVITY;
D O I：
10.1007/s00454-017-9938-z
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The random 2-dimensional simplicial complex process starts with a complete graph on n vertices, and in every step a new 2-dimensional face, chosen uniformly at random, is added. We prove that with probability tending to 1 as , the first homology group over vanishes at the very moment when all the edges are covered by triangular faces.
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页码：131 / 142
页数：12
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