Metastability in a condensing zero-range process in the thermodynamic limit

Autores
Armendáriz, María Inés; Grosskinsky, Stefan; Loulakis, Michail
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process of the rescaled location converges to a limiting Markov process on the unit torus. This process has stationary, independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice. Our result extends previous work for fixed lattices and diverging density [In: Beltran and Landim, Probab Theory Relat Fields 152(3–4):781–807, 2012], and we follow the martingale approach developed there and in subsequent publications. Besides additional technical difficulties in estimating error bounds for transition rates, the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells, corresponding to a typical set of configurations with a particular condensate location. The total exit rates from individual wells turn out to diverge in the limit, which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator. Another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells, which is of a general nature and can be adapted to other models.
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: Grosskinsky, Stefan. University of Warwick; Reino Unido
Fil: Loulakis, Michail. National Technical University of Athens; Grecia
Materia
Condensation
Metastability
Zero Range Process
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:11336/60127

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spelling Metastability in a condensing zero-range process in the thermodynamic limitArmendáriz, María InésGrosskinsky, StefanLoulakis, MichailCondensationMetastabilityZero Range Processhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process of the rescaled location converges to a limiting Markov process on the unit torus. This process has stationary, independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice. Our result extends previous work for fixed lattices and diverging density [In: Beltran and Landim, Probab Theory Relat Fields 152(3–4):781–807, 2012], and we follow the martingale approach developed there and in subsequent publications. Besides additional technical difficulties in estimating error bounds for transition rates, the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells, corresponding to a typical set of configurations with a particular condensate location. The total exit rates from individual wells turn out to diverge in the limit, which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator. Another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells, which is of a general nature and can be adapted to other models.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: Grosskinsky, Stefan. University of Warwick; Reino UnidoFil: Loulakis, Michail. National Technical University of Athens; GreciaSpringer2017-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/60127Armendáriz, María Inés; Grosskinsky, Stefan; Loulakis, Michail; Metastability in a condensing zero-range process in the thermodynamic limit; Springer; Probability Theory And Related Fields; 169; 1-2; 10-2017; 105-1750178-8051CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00440-016-0728-yinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00440-016-0728-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:54:15Zoai:ri.conicet.gov.ar:11336/60127instacron: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 09:54:15.347CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Metastability in a condensing zero-range process in the thermodynamic limit
title Metastability in a condensing zero-range process in the thermodynamic limit
spellingShingle Metastability in a condensing zero-range process in the thermodynamic limit
Armendáriz, María Inés
Condensation
Metastability
Zero Range Process
title_short Metastability in a condensing zero-range process in the thermodynamic limit
title_full Metastability in a condensing zero-range process in the thermodynamic limit
title_fullStr Metastability in a condensing zero-range process in the thermodynamic limit
title_full_unstemmed Metastability in a condensing zero-range process in the thermodynamic limit
title_sort Metastability in a condensing zero-range process in the thermodynamic limit
dc.creator.none.fl_str_mv Armendáriz, María Inés
Grosskinsky, Stefan
Loulakis, Michail
author Armendáriz, María Inés
author_facet Armendáriz, María Inés
Grosskinsky, Stefan
Loulakis, Michail
author_role author
author2 Grosskinsky, Stefan
Loulakis, Michail
author2_role author
author
dc.subject.none.fl_str_mv Condensation
Metastability
Zero Range Process
topic Condensation
Metastability
Zero Range Process
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process of the rescaled location converges to a limiting Markov process on the unit torus. This process has stationary, independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice. Our result extends previous work for fixed lattices and diverging density [In: Beltran and Landim, Probab Theory Relat Fields 152(3–4):781–807, 2012], and we follow the martingale approach developed there and in subsequent publications. Besides additional technical difficulties in estimating error bounds for transition rates, the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells, corresponding to a typical set of configurations with a particular condensate location. The total exit rates from individual wells turn out to diverge in the limit, which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator. Another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells, which is of a general nature and can be adapted to other models.
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: Grosskinsky, Stefan. University of Warwick; Reino Unido
Fil: Loulakis, Michail. National Technical University of Athens; Grecia
description Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process of the rescaled location converges to a limiting Markov process on the unit torus. This process has stationary, independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice. Our result extends previous work for fixed lattices and diverging density [In: Beltran and Landim, Probab Theory Relat Fields 152(3–4):781–807, 2012], and we follow the martingale approach developed there and in subsequent publications. Besides additional technical difficulties in estimating error bounds for transition rates, the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells, corresponding to a typical set of configurations with a particular condensate location. The total exit rates from individual wells turn out to diverge in the limit, which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator. Another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells, which is of a general nature and can be adapted to other models.
publishDate 2017
dc.date.none.fl_str_mv 2017-10
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/11336/60127
Armendáriz, María Inés; Grosskinsky, Stefan; Loulakis, Michail; Metastability in a condensing zero-range process in the thermodynamic limit; Springer; Probability Theory And Related Fields; 169; 1-2; 10-2017; 105-175
0178-8051
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60127
identifier_str_mv Armendáriz, María Inés; Grosskinsky, Stefan; Loulakis, Michail; Metastability in a condensing zero-range process in the thermodynamic limit; Springer; Probability Theory And Related Fields; 169; 1-2; 10-2017; 105-175
0178-8051
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00440-016-0728-y
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00440-016-0728-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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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/zip
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
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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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