Multistate voter model with imperfect copying
- Autores
- Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel
- Año de publicación
- 2019
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.
Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina
Fil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina - Materia
-
Complex Systems
Nonequilibrium statistical Mechanics
Active Matter
Social Systems - 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:11336/143150
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Multistate voter model with imperfect copyingVazquez, FedericoLoscar, Ernesto SelimBaglietto, GabrielComplex SystemsNonequilibrium statistical MechanicsActive MatterSocial Systemshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaAmerican Physical Society2019-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143150Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel; Multistate voter model with imperfect copying; American Physical Society; Physical Review E; 100; 4; 10-2019; 1-462470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.042301info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.042301info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.07253v2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:40Zoai:ri.conicet.gov.ar:11336/143150instacron: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 10:12:41.152CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Multistate voter model with imperfect copying |
title |
Multistate voter model with imperfect copying |
spellingShingle |
Multistate voter model with imperfect copying Vazquez, Federico Complex Systems Nonequilibrium statistical Mechanics Active Matter Social Systems |
title_short |
Multistate voter model with imperfect copying |
title_full |
Multistate voter model with imperfect copying |
title_fullStr |
Multistate voter model with imperfect copying |
title_full_unstemmed |
Multistate voter model with imperfect copying |
title_sort |
Multistate voter model with imperfect copying |
dc.creator.none.fl_str_mv |
Vazquez, Federico Loscar, Ernesto Selim Baglietto, Gabriel |
author |
Vazquez, Federico |
author_facet |
Vazquez, Federico Loscar, Ernesto Selim Baglietto, Gabriel |
author_role |
author |
author2 |
Loscar, Ernesto Selim Baglietto, Gabriel |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Complex Systems Nonequilibrium statistical Mechanics Active Matter Social Systems |
topic |
Complex Systems Nonequilibrium statistical Mechanics Active Matter Social Systems |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well. Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina Fil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina Fil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina |
description |
The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10 |
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/11336/143150 Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel; Multistate voter model with imperfect copying; American Physical Society; Physical Review E; 100; 4; 10-2019; 1-46 2470-0053 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/143150 |
identifier_str_mv |
Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel; Multistate voter model with imperfect copying; American Physical Society; Physical Review E; 100; 4; 10-2019; 1-46 2470-0053 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://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.042301 info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.042301 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.07253v2 |
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 application/pdf |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
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) |
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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 |