Topology of random geometric complexes: a survey

被引：1

作者：

Bobrowski O. ^{[1
]}

Kahle M. ^{[2
]}

机构：

[1] Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa

[2] Department of Mathematics, The Ohio State University, Columbus, OH

来源：

Journal of Applied and Computational Topology | 2018年 / 1卷 / 3-4期

关键词：

Boolean model; Homology; Random graphs; Random topology; Simplicial complexes;

D O I：

10.1007/s41468-017-0010-0

中图分类号：

学科分类号：

摘要：

In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes. Random geometric complexes may be viewed as higher-dimensional generalizations of random geometric graphs, where vertices are generated by a random point process, and edges are placed based on proximity. Extending the notion of connected components and cycles in graphs, the main object of study has been the homology of these complexes. We review the results known to date about the probabilistic behavior of the homology (and related structures) generated by these random complexes. © 2018, Springer International Publishing AG, part of Springer Nature.

引用

页码：331 / 364

页数：33

共 50 条

[1] Topology of random simplicial complexes: a survey
Kahle, Matthew
[J]. ALGEBRAIC TOPOLOGY: APPLICATIONS AND NEW DIRECTIONS, 2014, 620 : 201 - 221
[2] Random Geometric Complexes
Kahle, Matthew
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2011, 45 (03) : 553 - 573
[3] Random Geometric Complexes
Matthew Kahle
[J]. Discrete & Computational Geometry, 2011, 45 : 553 - 573
[4] SURVEY OF SOME RESULTS IN GEOMETRIC TOPOLOGY
SHER, RB
[J]. JOURNAL OF THE ELISHA MITCHELL SCIENTIFIC SOCIETY, 1976, 92 (03) : 98 - 103
[5] Topology of random clique complexes
Kahle, Matthew
[J]. DISCRETE MATHEMATICS, 2009, 309 (06) : 1658 - 1671
[6] Topology of Random 2-Complexes
D. Cohen
A. Costa
M. Farber
T. Kappeler
[J]. Discrete & Computational Geometry, 2012, 47 : 117 - 149
[7] Topology of Random 2-Complexes
Cohen, D.
Costa, A.
Farber, M.
Kappeler, T.
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 47 (01) : 117 - 149
[8] Random geometric complexes in the thermodynamic regime
Yogeshwaran, D.
Subag, Eliran
Adler, Robert J.
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2017, 167 (1-2) : 107 - 142
[9] Random geometric complexes in the thermodynamic regime
D. Yogeshwaran
Eliran Subag
Robert J. Adler
[J]. Probability Theory and Related Fields, 2017, 167 : 107 - 142
[10] GEOMETRIC TOPOLOGY AND SHAPE THEORY - SURVEY OF PROBLEMS AND RESULTS
BALL, BJ
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 82 (06) : 791 - 804

← 1 2 3 4 5 →