Nucleation and growth in two dimensions

Autores
Bollobás, Béla; Griffiths, Simon; Morris, Robert; Trivellato Rolla, Leonardo; Smith, Paul
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a dynamical process on a graph G, in which vertices are infected (randomly) at a rate which depends on the number of their neighbors that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z^2, significantly sharpening results of Dehghanpour and Schonmann. In particular, we determine the typical infection time up to a constant factor for almost all natural values of the parameters, and in a large range we obtain a stronger, sharp threshold.
Fil: Bollobás, Béla. University of Cambridge; Estados Unidos. University of Memphis; Estados Unidos
Fil: Griffiths, Simon. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil
Fil: Morris, Robert. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil
Fil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Smith, Paul. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil
Materia
NUCLEATION AND GROWTH
BOOTSTRAP PERCOLATION
FIRST PASSAGE PERCOLATION
RELAXATION TIME
KESTEN–SCHONMANN MODEL
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/136209
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/136209
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Nucleation and growth in two dimensionsBollobás, BélaGriffiths, SimonMorris, RobertTrivellato Rolla, LeonardoSmith, PaulNUCLEATION AND GROWTHBOOTSTRAP PERCOLATIONFIRST PASSAGE PERCOLATIONRELAXATION TIMEKESTEN–SCHONMANN MODELhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a dynamical process on a graph G, in which vertices are infected (randomly) at a rate which depends on the number of their neighbors that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z^2, significantly sharpening results of Dehghanpour and Schonmann. In particular, we determine the typical infection time up to a constant factor for almost all natural values of the parameters, and in a large range we obtain a stronger, sharp threshold.Fil: Bollobás, Béla. University of Cambridge; Estados Unidos. University of Memphis; Estados UnidosFil: Griffiths, Simon. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; BrasilFil: Morris, Robert. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; BrasilFil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Smith, Paul. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; BrasilJohn Wiley & Sons Inc2019-10-22info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/136209Bollobás, Béla; Griffiths, Simon; Morris, Robert; Trivellato Rolla, Leonardo; Smith, Paul; Nucleation and growth in two dimensions; John Wiley & Sons Inc; Random Structures Algorithms; 56; 1; 22-10-2019; 63-961042-9832CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20888info:eu-repo/semantics/altIdentifier/doi/10.1002/rsa.20888info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1508.06267info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:02:05Zoai:ri.conicet.gov.ar:11336/136209instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:02:06.143CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nucleation and growth in two dimensions
title Nucleation and growth in two dimensions
spellingShingle Nucleation and growth in two dimensions
Bollobás, Béla
NUCLEATION AND GROWTH
BOOTSTRAP PERCOLATION
FIRST PASSAGE PERCOLATION
RELAXATION TIME
KESTEN–SCHONMANN MODEL
title_short Nucleation and growth in two dimensions
title_full Nucleation and growth in two dimensions
title_fullStr Nucleation and growth in two dimensions
title_full_unstemmed Nucleation and growth in two dimensions
title_sort Nucleation and growth in two dimensions
dc.creator.none.fl_str_mv Bollobás, Béla
Griffiths, Simon
Morris, Robert
Trivellato Rolla, Leonardo
Smith, Paul
author Bollobás, Béla
author_facet Bollobás, Béla
Griffiths, Simon
Morris, Robert
Trivellato Rolla, Leonardo
Smith, Paul
author_role author
author2 Griffiths, Simon
Morris, Robert
Trivellato Rolla, Leonardo
Smith, Paul
author2_role author
author
author
author
dc.subject.none.fl_str_mv NUCLEATION AND GROWTH
BOOTSTRAP PERCOLATION
FIRST PASSAGE PERCOLATION
RELAXATION TIME
KESTEN–SCHONMANN MODEL
topic NUCLEATION AND GROWTH
BOOTSTRAP PERCOLATION
FIRST PASSAGE PERCOLATION
RELAXATION TIME
KESTEN–SCHONMANN MODEL
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider a dynamical process on a graph G, in which vertices are infected (randomly) at a rate which depends on the number of their neighbors that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z^2, significantly sharpening results of Dehghanpour and Schonmann. In particular, we determine the typical infection time up to a constant factor for almost all natural values of the parameters, and in a large range we obtain a stronger, sharp threshold.
Fil: Bollobás, Béla. University of Cambridge; Estados Unidos. University of Memphis; Estados Unidos
Fil: Griffiths, Simon. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil
Fil: Morris, Robert. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil
Fil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Smith, Paul. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil
description We consider a dynamical process on a graph G, in which vertices are infected (randomly) at a rate which depends on the number of their neighbors that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z^2, significantly sharpening results of Dehghanpour and Schonmann. In particular, we determine the typical infection time up to a constant factor for almost all natural values of the parameters, and in a large range we obtain a stronger, sharp threshold.
publishDate 2019
dc.date.none.fl_str_mv 2019-10-22
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/136209
Bollobás, Béla; Griffiths, Simon; Morris, Robert; Trivellato Rolla, Leonardo; Smith, Paul; Nucleation and growth in two dimensions; John Wiley & Sons Inc; Random Structures Algorithms; 56; 1; 22-10-2019; 63-96
1042-9832
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136209
identifier_str_mv Bollobás, Béla; Griffiths, Simon; Morris, Robert; Trivellato Rolla, Leonardo; Smith, Paul; Nucleation and growth in two dimensions; John Wiley & Sons Inc; Random Structures Algorithms; 56; 1; 22-10-2019; 63-96
1042-9832
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20888
info:eu-repo/semantics/altIdentifier/doi/10.1002/rsa.20888
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1508.06267
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons Inc
publisher.none.fl_str_mv John Wiley & Sons Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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