Open Access
August 2018 Exceptional times of the critical dynamical Erdős–Rényi graph
Matthew I. Roberts, Batı Şengül
Ann. Appl. Probab. 28(4): 2275-2308 (August 2018). DOI: 10.1214/17-AAP1357

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 (Gt:t[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 n2/3log1/3n with high probability. This is in contrast to the largest component in the static critical Erdős–Rényi graph, which is of order n2/3.

Citation

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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

Information

Received: 1 October 2016; Revised: 1 August 2017; Published: August 2018
First available in Project Euclid: 9 August 2018

zbMATH: 06974751
MathSciNet: MR3843829
Digital Object Identifier: 10.1214/17-AAP1357

Subjects:
Primary: 05C80 , 60F17 , 82C20

Keywords: dynamical random graphs , Erdős–Renyi , Giant component , Noise sensitivity , temporal networks

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.28 • No. 4 • August 2018
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