Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/fractal-geometry-and-stochastics-vi-asymptotics-of-integrals-of-betti-wtIcpzRwHl
References (21)
-
A. Costa, M. Farber (2014)
Random Simplicial ComplexesarXiv: Algebraic Topology
-
P. Erdos, A. Rényi (1984)
On the evolution of random graphsTransactions of the American Mathematical Society, 286
-
W. Ballmann, Jacek tkowski (1997)
On L2-cohomology and Property (T) for Automorphism Groups of Polyhedral Cell ComplexesGeometric and Functional Analysis, 7
-
Matthew Kahle (2012)
Sharp vanishing thresholds for cohomology of random flag complexesarXiv: Algebraic Topology
-
B. Bollobás (2001)
Random Graphs, Second Edition, 73
-
S. Janson, Johan Wästlund (2006)
Addendum to “The Minimal Spanning Tree in a Complete Graph and a Functional Limit Theorem for Trees in a Random Graph”Random Structures & Algorithms, 28
-
C. Hoffman, Matthew Kahle, Elliot Paquette (2012)
Spectral Gaps of Random Graphs and ApplicationsInternational Mathematics Research Notices
-
L Addario-Berry (2017)
3075Ann. Probab., 45
-
L. Addario-Berry, N. Broutin, C. Goldschmidt, G. Miermont (2013)
The local weak limit of the minimum spanning tree of the complete grapharXiv: Probability
-
K. Panagiotou, Benedikt Stufler, Kerstin Weller (2014)
Scaling Limits of Random Graphs from Subcritical ClassesarXiv: Probability
-
A. Zomorodian, G. Carlsson (2004)
Computing Persistent HomologyDiscrete & Computational Geometry, 33
-
A. Frieze (1985)
On the value of a random minimum spanning tree problemDiscret. Appl. Math., 10
-
Michael Schweinberger (2019)
Random GraphsFoundations of Data Science
-
M. Hino, Shu Kanazawa (2018)
Asymptotic behavior of lifetime sums for random simplicial complex processesJournal of the Mathematical Society of Japan
-
Y. Hiraoka, T. Shirai (2015)
Minimum spanning acycle and lifetime of persistent homology in the Linial–Meshulam processRandom Structures & Algorithms, 51
-
Matthew Kahle (2013)
Topology of random simplicial complexes: a surveyarXiv: Algebraic Topology
-
Christopher Fowler (2019)
Homology of Multi-Parameter Random Simplicial ComplexesDiscrete & Computational Geometry, 62
-
H. Garland (1973)
p-Adic Curvature and the Cohomology of Discrete Subgroups of p-Adic GroupsAnnals of Mathematics, 97
-
J. Kruskal (1956)
On the shortest spanning subtree of a graph and the traveling salesman problem, 7
-
Matthew Kahle (2006)
Topology of random clique complexesDiscret. Math., 309
-
N. Linial, R. Meshulam (2006)
Homological Connectivity Of Random 2-ComplexesCombinatorica, 26
- Publisher
- Springer International Publishing
- Copyright
- © Springer Nature Switzerland AG 2021
- ISBN
- 978-3-030-59648-4
- Pages
- 125 –140
- DOI
- 10.1007/978-3-030-59649-1_6
- Publisher site
- See Chapter on Publisher Site
Abstract
[We discuss a higher-dimensional analogue of Frieze’s ζ(3)-limit theorem for the Erdős–Rényi graph process applied to a family of increasing random simplicial complexes. In particular, we consider the time integrals of Betti numbers, which are interpreted as lifetime sums in the context of persistent homologies. We survey some recent results regarding their asymptotic behavior that answer some questions posed in an earlier study by Hiraoka and Shirai.]
Published: Mar 24, 2021
Keywords: Random simplicial complex; Betti number; Persistent homology; Lifetime sum; Primary: 60D05; Secondary: 05C80; 55U10; 05E45; 60C05