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

Yuhei Yamada; Yoshihiro Yamazaki

doi:10.7566/JPSJ.87.085002

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

Research output: Contribution to journal › Article › peer-review

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 language	English
Article number	085002
Journal	Journal of the Physical Society of Japan
Volume	87
Issue number	8
DOIs	https://doi.org/10.7566/JPSJ.87.085002
Publication status	Published - 2018 Jan 1

ASJC Scopus subject areas

Physics and Astronomy(all)

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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.",

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