Gaussian random permutation and the boson point process

Autores
Armendáriz, María Inés; Ferrari, Pablo Augusto; Yuhjtman, Sergio Andrés
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We construct an infinite volume spatial random permutation (χ,σ), where χ⊂ℝd is a point process and σ:χ→χ is a permutation (bijection), associated to the formal Hamiltonian H(χ,σ)=∑_x∈χ‖x−σ(x)‖2. The measures are parametrized by the density ρ of points and the temperature α. Feynman (1953) related spatial random permutations with boson systems and proposed that Bose-Einstein condensation occurs precisely when infinite cycles appear in the corresponding random permutation. Each finite cycle of σ induces a loop of points of χ. For ρ ≤ ρc we define (χ, σ) as a Poisson process of finite unrooted loops that we call Gaussian loop soup, analogous to the Brownian loop soup of Lawler and Werner (2004). We also construct Gaussian random interlacements, a Poisson process of double-infinite trajectories of random walks with Gaussian increments analogous to the Brownian random interlacements of Sznitman (2007). For d ≥ 3 and ρ > ρc we define (χ, σ) as the superposition of independent realizations of the Gaussian loop soup at density ρc and the Gaussian random interlacements at density ρ − ρc and call it a Gaussian random permutation at density ρ and temperature α. The resulting measure is Gibbs for the Hamiltonian H and the point marginal χ has the same distribution as the boson point process introduced by Macchi (1975) in the subcritical case and by Tamura-Ito (2007) in the supercritical case. Bose-Einstein condensation occurs when the Gaussian random permutation exhibits infinite trajectories.
Fil: Armendáriz, María Inés. 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: 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: Yuhjtman, Sergio Andrés. 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
Materia
SPATIAL RANDOM PERMUTATIONS
BOSE GAS
BOSON PROCESS
RANDOM INTERLACEMENTS
LOOP SOUP
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:11336/136897
Acceder
id CONICETDig_29fef8bc99aec83144bc0d1703432da7
oai_identifier_str oai:ri.conicet.gov.ar:11336/136897
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Gaussian random permutation and the boson point processArmendáriz, María InésFerrari, Pablo AugustoYuhjtman, Sergio AndrésSPATIAL RANDOM PERMUTATIONSBOSE GASBOSON PROCESSRANDOM INTERLACEMENTSLOOP SOUPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We construct an infinite volume spatial random permutation (χ,σ), where χ⊂ℝd is a point process and σ:χ→χ is a permutation (bijection), associated to the formal Hamiltonian H(χ,σ)=∑_x∈χ‖x−σ(x)‖2. The measures are parametrized by the density ρ of points and the temperature α. Feynman (1953) related spatial random permutations with boson systems and proposed that Bose-Einstein condensation occurs precisely when infinite cycles appear in the corresponding random permutation. Each finite cycle of σ induces a loop of points of χ. For ρ ≤ ρc we define (χ, σ) as a Poisson process of finite unrooted loops that we call Gaussian loop soup, analogous to the Brownian loop soup of Lawler and Werner (2004). We also construct Gaussian random interlacements, a Poisson process of double-infinite trajectories of random walks with Gaussian increments analogous to the Brownian random interlacements of Sznitman (2007). For d ≥ 3 and ρ > ρc we define (χ, σ) as the superposition of independent realizations of the Gaussian loop soup at density ρc and the Gaussian random interlacements at density ρ − ρc and call it a Gaussian random permutation at density ρ and temperature α. The resulting measure is Gibbs for the Hamiltonian H and the point marginal χ has the same distribution as the boson point process introduced by Macchi (1975) in the subcritical case and by Tamura-Ito (2007) in the supercritical case. Bose-Einstein condensation occurs when the Gaussian random permutation exhibits infinite trajectories.Fil: Armendáriz, María Inés. 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: 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: Yuhjtman, Sergio Andrés. 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"; ArgentinaCornell University2019-06info: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/11336/136897Armendáriz, María Inés; Ferrari, Pablo Augusto; Yuhjtman, Sergio Andrés; Gaussian random permutation and the boson point process; Cornell University; arXiv; 6-2019; 1-322331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1906.11120info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:08Zoai:ri.conicet.gov.ar:11336/136897instacron: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 09:36:08.735CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Gaussian random permutation and the boson point process
title Gaussian random permutation and the boson point process
spellingShingle Gaussian random permutation and the boson point process
Armendáriz, María Inés
SPATIAL RANDOM PERMUTATIONS
BOSE GAS
BOSON PROCESS
RANDOM INTERLACEMENTS
LOOP SOUP
title_short Gaussian random permutation and the boson point process
title_full Gaussian random permutation and the boson point process
title_fullStr Gaussian random permutation and the boson point process
title_full_unstemmed Gaussian random permutation and the boson point process
title_sort Gaussian random permutation and the boson point process
dc.creator.none.fl_str_mv Armendáriz, María Inés
Ferrari, Pablo Augusto
Yuhjtman, Sergio Andrés
author Armendáriz, María Inés
author_facet Armendáriz, María Inés
Ferrari, Pablo Augusto
Yuhjtman, Sergio Andrés
author_role author
author2 Ferrari, Pablo Augusto
Yuhjtman, Sergio Andrés
author2_role author
author
dc.subject.none.fl_str_mv SPATIAL RANDOM PERMUTATIONS
BOSE GAS
BOSON PROCESS
RANDOM INTERLACEMENTS
LOOP SOUP
topic SPATIAL RANDOM PERMUTATIONS
BOSE GAS
BOSON PROCESS
RANDOM INTERLACEMENTS
LOOP SOUP
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 construct an infinite volume spatial random permutation (χ,σ), where χ⊂ℝd is a point process and σ:χ→χ is a permutation (bijection), associated to the formal Hamiltonian H(χ,σ)=∑_x∈χ‖x−σ(x)‖2. The measures are parametrized by the density ρ of points and the temperature α. Feynman (1953) related spatial random permutations with boson systems and proposed that Bose-Einstein condensation occurs precisely when infinite cycles appear in the corresponding random permutation. Each finite cycle of σ induces a loop of points of χ. For ρ ≤ ρc we define (χ, σ) as a Poisson process of finite unrooted loops that we call Gaussian loop soup, analogous to the Brownian loop soup of Lawler and Werner (2004). We also construct Gaussian random interlacements, a Poisson process of double-infinite trajectories of random walks with Gaussian increments analogous to the Brownian random interlacements of Sznitman (2007). For d ≥ 3 and ρ > ρc we define (χ, σ) as the superposition of independent realizations of the Gaussian loop soup at density ρc and the Gaussian random interlacements at density ρ − ρc and call it a Gaussian random permutation at density ρ and temperature α. The resulting measure is Gibbs for the Hamiltonian H and the point marginal χ has the same distribution as the boson point process introduced by Macchi (1975) in the subcritical case and by Tamura-Ito (2007) in the supercritical case. Bose-Einstein condensation occurs when the Gaussian random permutation exhibits infinite trajectories.
Fil: Armendáriz, María Inés. 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: 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: Yuhjtman, Sergio Andrés. 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
description We construct an infinite volume spatial random permutation (χ,σ), where χ⊂ℝd is a point process and σ:χ→χ is a permutation (bijection), associated to the formal Hamiltonian H(χ,σ)=∑_x∈χ‖x−σ(x)‖2. The measures are parametrized by the density ρ of points and the temperature α. Feynman (1953) related spatial random permutations with boson systems and proposed that Bose-Einstein condensation occurs precisely when infinite cycles appear in the corresponding random permutation. Each finite cycle of σ induces a loop of points of χ. For ρ ≤ ρc we define (χ, σ) as a Poisson process of finite unrooted loops that we call Gaussian loop soup, analogous to the Brownian loop soup of Lawler and Werner (2004). We also construct Gaussian random interlacements, a Poisson process of double-infinite trajectories of random walks with Gaussian increments analogous to the Brownian random interlacements of Sznitman (2007). For d ≥ 3 and ρ > ρc we define (χ, σ) as the superposition of independent realizations of the Gaussian loop soup at density ρc and the Gaussian random interlacements at density ρ − ρc and call it a Gaussian random permutation at density ρ and temperature α. The resulting measure is Gibbs for the Hamiltonian H and the point marginal χ has the same distribution as the boson point process introduced by Macchi (1975) in the subcritical case and by Tamura-Ito (2007) in the supercritical case. Bose-Einstein condensation occurs when the Gaussian random permutation exhibits infinite trajectories.
publishDate 2019
dc.date.none.fl_str_mv 2019-06
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/11336/136897
Armendáriz, María Inés; Ferrari, Pablo Augusto; Yuhjtman, Sergio Andrés; Gaussian random permutation and the boson point process; Cornell University; arXiv; 6-2019; 1-32
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136897
identifier_str_mv Armendáriz, María Inés; Ferrari, Pablo Augusto; Yuhjtman, Sergio Andrés; Gaussian random permutation and the boson point process; Cornell University; arXiv; 6-2019; 1-32
2331-8422
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://arxiv.org/abs/1906.11120
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 Cornell University
publisher.none.fl_str_mv Cornell University
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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