Occupation times of long-range exclusion and connections to KPZ class exponents
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
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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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 |
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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 |
repository.mail.fl_str_mv |
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