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          Institute: MPI für Dynamik und Selbstorganisation     Collection: Nichtlineare Dynamik     Display Documents

ID: 673708.0, MPI für Dynamik und Selbstorganisation / Nichtlineare Dynamik
Phase transitions in supercritical explosive percolation
Authors:Chen, Wei; Nagler, Jan; Cheng, Xueqi; Jin, Xiaolong; Shen, Huawei; Zheng, Zhiming; D'Souza, Raissa M.
Date of Publication (YYYY-MM-DD):2013-05-24
Title of Journal:Physical Review E
Sequence Number of Article:052130
Review Status:Peer-review
Audience:Experts Only
Abstract / Description:Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of α, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime α∈[0.6,0.95] where it is known that only one giant component, denoted C1, initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime C1 stops growing and eventually a second giant component, denoted C2, emerges in a continuous percolation transition. The delay between the emergence of C1 and C2 and their asymptotic sizes both depend on the value of α and we establish by several techniques that there exists a bifurcation point αc=0.763±0.002. For α∈[0.6,αc), C1 stops growing the instant it emerges and the delay between the emergence of C1 and C2 decreases with increasing α. For α∈(αc,0.95], in contrast, C1 continues growing into the supercritical regime and the delay between the emergence of C1 and C2 increases with increasing α. As we show, αc marks the minimal delay possible between the emergence of C1 and C2 (i.e., the smallest edge density for which C2 can exist). We also establish many features of the continuous percolation of C2 including scaling exponents and relations.
External Publication Status:published
Document Type:Article
Communicated by:Folkert Müller-Hoissen
Affiliations:MPI für Dynamik und Selbstorganisation/Nichtlineare Dynamik
External Affiliations:School of Mathematical Sciences, Peking University, Beijing, China
Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
University of California, Davis, California 95616, USA
Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, Göttingen, Germany
Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing University of Aeronautics and Astronautics, 100191 Beijing, China
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