Occupation times of long-range exclusion and connections to KPZ class exponents

Detalhes bibliográficos
Autor(a) principal: Bernardin, Cédric
Data de Publicação: 2016
Outros Autores: Gonçalves, Patrícia, Sethuraman, Sunder
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/35190
Resumo: With respect to a class of long-range exclusion processes on $\ZZ^d$, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on $\alpha$, $d$ and $\rho$ with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter $H\in [1/2,3/4]$. However, in the asymmetric case, we study the asymptotics of the variances, which when $d=1$ and $\rho=1/2$ points to a curious dichotomy between long-range strength parameters $0<\alpha\leq 3/2$ and $\alpha>3/2$. In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.
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spelling Occupation times of long-range exclusion and connections to KPZ class exponentsAdditive functionalOccupation timeKPZ classExponentLong-rangeSimpleExclusionCiências Naturais::MatemáticasScience & TechnologyWith respect to a class of long-range exclusion processes on $\ZZ^d$, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on $\alpha$, $d$ and $\rho$ with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter $H\in [1/2,3/4]$. However, in the asymmetric case, we study the asymptotics of the variances, which when $d=1$ and $\rho=1/2$ points to a curious dichotomy between long-range strength parameters $0<\alpha\leq 3/2$ and $\alpha>3/2$. In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.The research of CB was supported in part by the French Ministry of Education through the grant ANR JCJC EDNHS. PG thanks FCT (Portugal) for support through the research project PTDC/MAT/109844/2009 and CNPq (Brazil) for support through the research project 480431/2013-2. PG thanks CMAT for support by "FEDER" through the "Programa Operacional Factores de Competitividade COMPETE" and by FCT through the project PEst-C/MAT/UI0013/2011. SS was supported in part by ARO grant W911NF-14-1-0179.Springer VerlagUniversidade do MinhoBernardin, CédricGonçalves, PatríciaSethuraman, Sunder20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/35190engBernardin, C., Goncalves, P., & Sethuraman, S. (2016). Occupation times of long-range exclusion and connections to KPZ class exponents. Probability Theory and Related Fields, 166(1-2), 365-428. doi: 10.1007/s00440-015-0661-50178-805110.1007/s00440-015-0661-5info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:38:09Zoai:repositorium.sdum.uminho.pt:1822/35190Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:34:32.648542Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Occupation times of long-range exclusion and connections to KPZ class exponents
title Occupation times of long-range exclusion and connections to KPZ class exponents
spellingShingle Occupation times of long-range exclusion and connections to KPZ class exponents
Bernardin, Cédric
Additive functional
Occupation time
KPZ class
Exponent
Long-range
Simple
Exclusion
Ciências Naturais::Matemáticas
Science & Technology
title_short Occupation times of long-range exclusion and connections to KPZ class exponents
title_full Occupation times of long-range exclusion and connections to KPZ class exponents
title_fullStr Occupation times of long-range exclusion and connections to KPZ class exponents
title_full_unstemmed Occupation times of long-range exclusion and connections to KPZ class exponents
title_sort Occupation times of long-range exclusion and connections to KPZ class exponents
author Bernardin, Cédric
author_facet Bernardin, Cédric
Gonçalves, Patrícia
Sethuraman, Sunder
author_role author
author2 Gonçalves, Patrícia
Sethuraman, Sunder
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Bernardin, Cédric
Gonçalves, Patrícia
Sethuraman, Sunder
dc.subject.por.fl_str_mv Additive functional
Occupation time
KPZ class
Exponent
Long-range
Simple
Exclusion
Ciências Naturais::Matemáticas
Science & Technology
topic Additive functional
Occupation time
KPZ class
Exponent
Long-range
Simple
Exclusion
Ciências Naturais::Matemáticas
Science & Technology
description With respect to a class of long-range exclusion processes on $\ZZ^d$, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on $\alpha$, $d$ and $\rho$ with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter $H\in [1/2,3/4]$. However, in the asymmetric case, we study the asymptotics of the variances, which when $d=1$ and $\rho=1/2$ points to a curious dichotomy between long-range strength parameters $0<\alpha\leq 3/2$ and $\alpha>3/2$. In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/35190
url http://hdl.handle.net/1822/35190
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bernardin, C., Goncalves, P., & Sethuraman, S. (2016). Occupation times of long-range exclusion and connections to KPZ class exponents. Probability Theory and Related Fields, 166(1-2), 365-428. doi: 10.1007/s00440-015-0661-5
0178-8051
10.1007/s00440-015-0661-5
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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