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Abstract
In this paper we introduce a network model which evolves in time, and study its largest connected component. We consider a process of graphs (G_t : t∈[0,1]), where initially we start with a critical Erdös-Rényi graph ER(n, 1/n), and then evolve forwards in time by resampling each edge independently at rate 1. We show that the size of the largest connected component that appears during the time interval [0,1] is of order n^{2/3}log^{1/3}n with high probability. This is in contrast to the largest component in the static critical Erdös-Rényi graph, which is of order n^{2/3}.
Original language | English |
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Pages (from-to) | 2275-2308 |
Number of pages | 34 |
Journal | Annals of Applied Probability |
Volume | 28 |
Issue number | 4 |
Early online date | 9 Aug 2018 |
DOIs | |
Publication status | Published - 31 Aug 2018 |
Keywords
- Dynamical random graphs
- Erdos–Renyi
- Giant component
- Noise sensitivity
- Temporal networks
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Dive into the research topics of 'Exceptional times of the critical dynamical Erdős-Rényi graph'. Together they form a unique fingerprint.Projects
- 1 Finished
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EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts
Roberts, M. (PI)
Engineering and Physical Sciences Research Council
3/04/13 → 2/07/16
Project: Research council
Profiles
-
Matt Roberts
- Department of Mathematical Sciences - Royal Society University Research Fellow
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath
Person: Research & Teaching