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dc.contributor.author
Armendáriz, María Inés
dc.contributor.author
Grosskinsky, Stefan
dc.contributor.author
Loulakis, Michail
dc.date.available
2018-09-18T19:34:56Z
dc.date.issued
2017-10
dc.identifier.citation
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
dc.identifier.issn
0178-8051
dc.identifier.uri
http://hdl.handle.net/11336/60127
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Condensation
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Metastability
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Zero Range Process
dc.subject.classification
Matemática Pura
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Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Metastability in a condensing zero-range process in the thermodynamic limit
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-09-18T14:15:23Z
dc.journal.volume
169
dc.journal.number
1-2
dc.journal.pagination
105-175
dc.journal.pais
Alemania
dc.journal.ciudad
Berlin
dc.description.fil
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
dc.description.fil
Fil: Grosskinsky, Stefan. University of Warwick; Reino Unido
dc.description.fil
Fil: Loulakis, Michail. National Technical University of Athens; Grecia
dc.journal.title
Probability Theory And Related Fields
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://dx.doi.org/10.1007/s00440-016-0728-y
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00440-016-0728-y
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