Condition of weak discontinuity for percolation models with edge selection rule depending on cluster sizes

Yuhei Yamada, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    Abstract

    With regard to rapid transition in percolation on graphs, a sufficient condition for cluster sizes to realize the weak discontinuity is derived. We focused on a group of models in which edges are added between nodes with a probability depending on their cluster sizes. It is found that the Erdös–Rényi model becomes weakly discontinuous depending on some initial condition.

    Original languageEnglish
    Article number085002
    JournalJournal of the Physical Society of Japan
    Volume87
    Issue number8
    DOIs
    Publication statusPublished - 2018 Jan 1

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    discontinuity

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

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    title = "Condition of weak discontinuity for percolation models with edge selection rule depending on cluster sizes",
    abstract = "With regard to rapid transition in percolation on graphs, a sufficient condition for cluster sizes to realize the weak discontinuity is derived. We focused on a group of models in which edges are added between nodes with a probability depending on their cluster sizes. It is found that the Erd{\"o}s–R{\'e}nyi model becomes weakly discontinuous depending on some initial condition.",
    author = "Yuhei Yamada and Yoshihiro Yamazaki",
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    AU - Yamazaki, Yoshihiro

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    AB - With regard to rapid transition in percolation on graphs, a sufficient condition for cluster sizes to realize the weak discontinuity is derived. We focused on a group of models in which edges are added between nodes with a probability depending on their cluster sizes. It is found that the Erdös–Rényi model becomes weakly discontinuous depending on some initial condition.

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