On the evolution of topology in dynamic clique complexes

Article Type

Research Article

Publication Title

Advances in Applied Probability

Abstract

We consider a time varying analogue of the ErdÅ's-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=n α, 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→.

First Page

989

Last Page

1014

DOI

10.1017/apr.2016.62

Publication Date

12-1-2016

Comments

Open Access; Green Open Access

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