THE THRESHOLD FUNCTION FOR VANISHING OF THE TOP HOMOLOGY GROUP OF RANDOM d-COMPLEXES

被引：18

作者：

Kozlov, Dmitry N. ^{[1
]}

机构：

[1] Univ Bremen, Dept Math, D-28334 Bremen, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 12期

关键词：

Random simplicial complexes; threshold function; second moment method; homology; CONNECTIVITY; TOPOLOGY;

D O I：

10.1090/S0002-9939-2010-10596-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For positive integers n and cl, and the probability function 0 <= P(n) <= 1, we let Y(n,p,d) denote the probability space of all at most d-dimensional simplicial complexes on n vertices, which contain the full (d 1)-dimensional skeleton, and whose d-simplices appear with probability p(n). In this paper we determine the threshold function for vanishing of the top homology group in Y(n,p,d), for all d >= 1.

引用

页码：4517 / 4527

页数：11

共 4 条

[1] The Threshold for Integer Homology in Random d-Complexes
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Kahle, Matthew
Paquette, Elliot
DISCRETE & COMPUTATIONAL GEOMETRY, 2017, 57 (04) : 810 - 823
[2] The Threshold for Integer Homology in Random d-Complexes
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Matthew Kahle
Elliot Paquette
Discrete & Computational Geometry, 2017, 57 : 810 - 823
[3] On the Vanishing of Homology in Random Cech Complexes
Bobrowski, Omer
Weinberger, Shmuel
RANDOM STRUCTURES & ALGORITHMS, 2017, 51 (01) : 14 - 51
[4] The threshold for d-collapsibility in random complexes*
Aronshtam, L.
Linial, N.
RANDOM STRUCTURES & ALGORITHMS, 2016, 48 (02) : 260 - 269

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