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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/136209
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:29:36Zoai: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:34982025-09-29 10:29:37.059CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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13.070432 |