Two Phase Transitions in Two-Way Bootstrap Percolation.

Ahad N. Zehmakan

doi:10.4230/LIPICS.ISAAC.2019.5

Two Phase Transitions in Two-Way Bootstrap Percolation.

Ahad N. Zehmakan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

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.

Original language	English
Title of host publication	Leibniz International Proceedings in Informatics (LIPIcs)
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	5:1-5:21
ISBN (Print)	978-3-95977-130-6
DOIs	https://doi.org/10.4230/LIPICS.ISAAC.2019.5
Publication status	Published - 2019
Externally published	Yes

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10.4230/LIPICS.ISAAC.2019.5

https://dblp.org/rec/conf/isaac/Zehmakan19

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title = "Two Phase Transitions in Two-Way Bootstrap Percolation.",

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.",

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PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.4230/LIPICS.ISAAC.2019.5

DO - 10.4230/LIPICS.ISAAC.2019.5

M3 - Conference contribution

SN - 978-3-95977-130-6

SP - 5:1-5:21

BT - Leibniz International Proceedings in Informatics (LIPIcs)

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -

Two Phase Transitions in Two-Way Bootstrap Percolation.

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