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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 ErdösRényi 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 ErdösRényi graph, which is of order n^{2/3}.
Original language  English 

Pages (fromto)  22752308 
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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Projects
 1 Finished

EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts
Engineering and Physical Sciences Research Council
3/04/13 → 2/07/16
Project: Research council
Profiles

Matthew Roberts
 Department of Mathematical Sciences  Royal Society University Research Fellow & Reader
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Probability Laboratory at Bath
Person: Research & Teaching