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On the evolution of topology in dynamic clique complexes

  • Gugan C. Thoppe (a1), D. Yogeshwaran (a2) and Robert J. Adler (a1)

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=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→∞.

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Corresponding author

* Postal address: Faculty of Electrical Engineering, Technion, Haifa, 32000, Israel.
** Email address: gugan.thoppe@gmail.com
*** Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, 560059, India.

References

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On the evolution of topology in dynamic clique complexes

  • Gugan C. Thoppe (a1), D. Yogeshwaran (a2) and Robert J. Adler (a1)

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