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December 2016 On the evolution of topology in dynamic clique complexes
Gugan C. Thoppe, D. Yogeshwaran, Robert J. Adler
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Adv. in Appl. Probab. 48(4): 989-1014 (December 2016).

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 determined by the edges, which evolve independently as continuous-time Markov chains. Our main result is that when the edge inclusion probability is of the form p=nα, where n is the number of vertices and α∈(-1/k, -1/(k + 1)), then the process of the normalised kth Betti number of these dynamic clique complexes converges weakly to the Ornstein–Uhlenbeck process as n→∞.

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Gugan C. Thoppe. D. Yogeshwaran. Robert J. Adler. "On the evolution of topology in dynamic clique complexes." Adv. in Appl. Probab. 48 (4) 989 - 1014, December 2016.

Information

Published: December 2016
First available in Project Euclid: 24 December 2016

zbMATH: 1356.05136
MathSciNet: MR3595763

Subjects:
Primary: 05C80
Secondary: 55U10, 60B10, 60C05

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 4 • December 2016
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