BBS invariant measures with independent soliton components

Autores
Ferrari, Pablo Augusto; Gabrielli, Davide
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Box-Ball System (BBS) is a one-dimensional cellular automaton in the configuration space { 0 , 1 } ^Z introduced by Takahashi and Satsuma [8], who identified conserved quantities called solitons. Ferrari, Nguyen, Rolla and Wang [4] map a configuration to a family of soliton components, indexed by the soliton sizes k ≥ 1 . Building over this decomposition, we give an explicit construction of a large family of invariant measures for the BBS that are also shift invariant, including Ising-like Markov and Bernoulli product measures. The construction is based on the concatenation of iid excursions of the associated walk trajectory. Each excursion has the property that the law of its k component given the larger components is product of a finite number of geometric distributions with a parameter depending on k . As a consequence, the law of each component of the resulting ball configuration is product of identically distributed geometric random variables, and the components are independent. This last property implies invariance for BBS, as shown by [4].
Fil: Ferrari, Pablo Augusto. 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: Gabrielli, Davide. Universita degli Studi dell'Aquila; Italia
Materia
BOX-BALL SYSTEM
CONSERVATIVE CELLULAR AUTOMATA
SOLITON COMPONENTS
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:11336/138101
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/138101
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling BBS invariant measures with independent soliton componentsFerrari, Pablo AugustoGabrielli, DavideBOX-BALL SYSTEMCONSERVATIVE CELLULAR AUTOMATASOLITON COMPONENTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The Box-Ball System (BBS) is a one-dimensional cellular automaton in the configuration space { 0 , 1 } ^Z introduced by Takahashi and Satsuma [8], who identified conserved quantities called solitons. Ferrari, Nguyen, Rolla and Wang [4] map a configuration to a family of soliton components, indexed by the soliton sizes k ≥ 1 . Building over this decomposition, we give an explicit construction of a large family of invariant measures for the BBS that are also shift invariant, including Ising-like Markov and Bernoulli product measures. The construction is based on the concatenation of iid excursions of the associated walk trajectory. Each excursion has the property that the law of its k component given the larger components is product of a finite number of geometric distributions with a parameter depending on k . As a consequence, the law of each component of the resulting ball configuration is product of identically distributed geometric random variables, and the components are independent. This last property implies invariance for BBS, as shown by [4].Fil: Ferrari, Pablo Augusto. 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: Gabrielli, Davide. Universita degli Studi dell'Aquila; ItaliaUniv Washington2020-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/138101Ferrari, Pablo Augusto; Gabrielli, Davide; BBS invariant measures with independent soliton components; Univ Washington; Electronic Journal Of Probability; 25; 6-2020; 1-261083-6489CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1812.02437info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:43Zoai:ri.conicet.gov.ar:11336/138101instacron: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 09:40:44.229CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv BBS invariant measures with independent soliton components
title BBS invariant measures with independent soliton components
spellingShingle BBS invariant measures with independent soliton components
Ferrari, Pablo Augusto
BOX-BALL SYSTEM
CONSERVATIVE CELLULAR AUTOMATA
SOLITON COMPONENTS
title_short BBS invariant measures with independent soliton components
title_full BBS invariant measures with independent soliton components
title_fullStr BBS invariant measures with independent soliton components
title_full_unstemmed BBS invariant measures with independent soliton components
title_sort BBS invariant measures with independent soliton components
dc.creator.none.fl_str_mv Ferrari, Pablo Augusto
Gabrielli, Davide
author Ferrari, Pablo Augusto
author_facet Ferrari, Pablo Augusto
Gabrielli, Davide
author_role author
author2 Gabrielli, Davide
author2_role author
dc.subject.none.fl_str_mv BOX-BALL SYSTEM
CONSERVATIVE CELLULAR AUTOMATA
SOLITON COMPONENTS
topic BOX-BALL SYSTEM
CONSERVATIVE CELLULAR AUTOMATA
SOLITON COMPONENTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Box-Ball System (BBS) is a one-dimensional cellular automaton in the configuration space { 0 , 1 } ^Z introduced by Takahashi and Satsuma [8], who identified conserved quantities called solitons. Ferrari, Nguyen, Rolla and Wang [4] map a configuration to a family of soliton components, indexed by the soliton sizes k ≥ 1 . Building over this decomposition, we give an explicit construction of a large family of invariant measures for the BBS that are also shift invariant, including Ising-like Markov and Bernoulli product measures. The construction is based on the concatenation of iid excursions of the associated walk trajectory. Each excursion has the property that the law of its k component given the larger components is product of a finite number of geometric distributions with a parameter depending on k . As a consequence, the law of each component of the resulting ball configuration is product of identically distributed geometric random variables, and the components are independent. This last property implies invariance for BBS, as shown by [4].
Fil: Ferrari, Pablo Augusto. 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: Gabrielli, Davide. Universita degli Studi dell'Aquila; Italia
description The Box-Ball System (BBS) is a one-dimensional cellular automaton in the configuration space { 0 , 1 } ^Z introduced by Takahashi and Satsuma [8], who identified conserved quantities called solitons. Ferrari, Nguyen, Rolla and Wang [4] map a configuration to a family of soliton components, indexed by the soliton sizes k ≥ 1 . Building over this decomposition, we give an explicit construction of a large family of invariant measures for the BBS that are also shift invariant, including Ising-like Markov and Bernoulli product measures. The construction is based on the concatenation of iid excursions of the associated walk trajectory. Each excursion has the property that the law of its k component given the larger components is product of a finite number of geometric distributions with a parameter depending on k . As a consequence, the law of each component of the resulting ball configuration is product of identically distributed geometric random variables, and the components are independent. This last property implies invariance for BBS, as shown by [4].
publishDate 2020
dc.date.none.fl_str_mv 2020-06
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/11336/138101
Ferrari, Pablo Augusto; Gabrielli, Davide; BBS invariant measures with independent soliton components; Univ Washington; Electronic Journal Of Probability; 25; 6-2020; 1-26
1083-6489
CONICET Digital
CONICET
url http://hdl.handle.net/11336/138101
identifier_str_mv Ferrari, Pablo Augusto; Gabrielli, Davide; BBS invariant measures with independent soliton components; Univ Washington; Electronic Journal Of Probability; 25; 6-2020; 1-26
1083-6489
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1812.02437
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
dc.publisher.none.fl_str_mv Univ Washington
publisher.none.fl_str_mv Univ Washington
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 13.070432

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