# Erratum: Limit theorems for Betti numbers of random simplicial complexes

@article{Kahle2015ErratumLT, title={Erratum: Limit theorems for Betti numbers of random simplicial complexes}, author={Matthew Kahle and Elizabeth S. Meckes}, journal={arXiv: Probability}, year={2015} }

We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".

## 8 Citations

Topology of random geometric complexes: a survey

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- 2018

This article surveys the rapidly emerging area of random geometric simplicial complexes, and reviews the results known to date about the probabilistic behavior of the homology (and related structures) generated by these random complexes.

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Abstract The objective of this study is to examine the asymptotic behavior of Betti numbers of Čech complexes treated as stochastic processes and formed from random points in the d-dimensional…

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The objective of this study is to examine the asymptotic behavior of Betti numbers of \v{C}ech complexes treated as stochastic processes and formed from random points in the $d$-dimensional Euclidean…

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Abstract We consider a time varying analogue of the Erdős–Rényi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationary and are…

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- MathematicsThe Annals of Applied Probability
- 2018

We investigate the topological dynamics of extreme sample clouds generated by a heavy tail distribution on R by establishing various limit theorems for Betti numbers, a basic quantifier of algebraic…

Limit Theorems for the Sum of Persistence Barcodes

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- 2016

Topological Data Analysis (TDA) refers to an approach that uses concepts from algebraic topology to study the "shapes" of datasets. The main focus of this paper is persistent homology, a ubiquitous…

On the evolution of topology in dynamic Erd} os-R enyi graphs

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- 2015

We study a time varying analogue of the Erd} os-R enyi graph, which we call the dynamic Erd} os-R enyi graph, and concentrate on the topological aspects of its clique complex. Denoting the graph on n…

Gigantic random simplicial complexes

- MathematicsHomology, Homotopy and Applications
- 2020

We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalence - it almost…

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