License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.5
URN: urn:nbn:de:0030-drops-115017
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11501/
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Zehmakan, Ahad N.

Two Phase Transitions in Two-Way Bootstrap Percolation

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LIPIcs-ISAAC-2019-5.pdf (0.7 MB)

Abstract

Consider a graph G and an initial random configuration, where each node is black with probability p and white otherwise, independently. In discrete-time rounds, each node becomes black if it has at least r black neighbors and white otherwise. We prove that this basic process exhibits a threshold behavior with two phase transitions when the underlying graph is a d-dimensional torus and identify the threshold values.

BibTeX - Entry

@InProceedings{zehmakan:LIPIcs:2019:11501,
  author =	{Ahad N. Zehmakan},
  title =	{{Two Phase Transitions in Two-Way Bootstrap Percolation}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11501},
  URN =		{urn:nbn:de:0030-drops-115017},
  doi =		{10.4230/LIPIcs.ISAAC.2019.5},
  annote =	{Keywords: bootstrap percolation, cellular automata, phase transition, d-dimensional torus, r-threshold model, biased majority}
}

Keywords: bootstrap percolation, cellular automata, phase transition, d-dimensional torus, r-threshold model, biased majority
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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