Threshold behavior of bootstrap percolation.

Ahad N. Zehmakan

doi:10.1016/J.DISC.2020.112211

Threshold behavior of bootstrap percolation.

Ahad N. Zehmakan

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

5 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
Number of pages	14
Journal	Discret. Math.
Volume	344
Issue number	2
DOIs	https://doi.org/10.1016/J.DISC.2020.112211
Publication status	Published - Jan 2021
Externally published	Yes

Access to Document

10.1016/J.DISC.2020.112211

https://dblp.org/rec/journals/dm/Zehmakan21

Cite this

@article{4b65de912b5b4a82b762befdbdf9407b,

title = "Threshold behavior of 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",

author = "Zehmakan, \{Ahad N.\}",

note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",

year = "2021",

month = jan,

doi = "10.1016/J.DISC.2020.112211",

language = "English",

volume = "344",

journal = "Discret. Math.",

number = "2",

}

TY - JOUR

T1 - Threshold behavior of bootstrap percolation.

AU - Zehmakan, Ahad N.

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2021/1

Y1 - 2021/1

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

UR - https://www.scopus.com/pages/publications/85096634710

U2 - 10.1016/J.DISC.2020.112211

DO - 10.1016/J.DISC.2020.112211

M3 - Article

VL - 344

JO - Discret. Math.

JF - Discret. Math.

IS - 2

ER -

Threshold behavior of bootstrap percolation.

Abstract

Access to Document

Other files and links

Fingerprint

Cite this