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 $(G_{t}:t\in [0,1])$, where initially we start with a critical Erdős–Rényi graph ER$(n,1/n)$, and then evolve forward 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 Erdős–Rényi graph, which is of order $n^{2/3}$.
Citation
Matthew I. Roberts. Batı Şengül. "Exceptional times of the critical dynamical Erdős–Rényi graph." Ann. Appl. Probab. 28 (4) 2275 - 2308, August 2018. https://doi.org/10.1214/17-AAP1357
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