Time fuctuations of the random average process with parabolic initial conditions

Detalhes bibliográficos
Autor(a) principal: Fontes, L.R.G.
Data de Publicação: 2003
Outros Autores: Medeiros, D.P., Vachkovskaia, M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFBA
Texto Completo: http://www.repositorio.ufba.br/ri/handle/ri/7324
Resumo: p. 257-276
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spelling Fontes, L.R.G.Medeiros, D.P.Vachkovskaia, M.Fontes, L.R.G.Medeiros, D.P.Vachkovskaia, M.2012-12-07T15:30:52Z2012-12-07T15:30:52Z20030304-4149http://www.repositorio.ufba.br/ri/handle/ri/7324v. 103, n. 2p. 257-276The random average process is a randomly evolving d-dimensional surface whose heights are updated by random convex combinations of neighboring heights. The !uctuations of this process in case of linear initial conditions have been studied before. In this paper, we analyze the case of polynomial initial conditions of degree 2 and higher. Speci8cally, we prove that the time !uctuations of a initial parabolic surface are of order n2−d=2 for d=1; 2; 3; log n in d=4; and are bounded in d¿5. We establish a central limit theorem in d = 1. In the bounded case of d¿5, we exhibit an invariant measure for the process as seen from the average height at the origin and describe its asymptotic space !uctuations. We consider brie!y the case of initial polynomial surfaces of higher degree to show that their time !uctuations are not bounded in high dimensions, in contrast with the linear and parabolic cases. c 2002 Elsevier Science B.V. All rights reserved.Submitted by Suelen Reis (suelen_suzane@hotmail.com) on 2012-12-07T15:30:52Z No. of bitstreams: 1 1-s2.0-S0304414902002107-main.pdf: 246212 bytes, checksum: 1fd0262f9086edca86a3ce77c3e0830b (MD5)Made available in DSpace on 2012-12-07T15:30:52Z (GMT). No. of bitstreams: 1 1-s2.0-S0304414902002107-main.pdf: 246212 bytes, checksum: 1fd0262f9086edca86a3ce77c3e0830b (MD5) Previous issue date: 2003http://dx.doi.org/10.1016/S0304-4149(02)00210-7reponame:Repositório Institucional da UFBAinstname:Universidade Federal da Bahia (UFBA)instacron:UFBARandom average processRandom surfacesHarness processLinear processSurface !uctuationsCentral limit theoremTime fuctuations of the random average process with parabolic initial conditionsStochastic Processes and their Applicationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleenginfo:eu-repo/semantics/openAccessORIGINAL1-s2.0-S0304414902002107-main.pdf1-s2.0-S0304414902002107-main.pdfapplication/pdf246212https://repositorio.ufba.br/bitstream/ri/7324/1/1-s2.0-S0304414902002107-main.pdf1fd0262f9086edca86a3ce77c3e0830bMD51LICENSElicense.txtlicense.txttext/plain1762https://repositorio.ufba.br/bitstream/ri/7324/2/license.txt1b89a9a0548218172d7c829f87a0eab9MD52TEXT1-s2.0-S0304414902002107-main.pdf.txt1-s2.0-S0304414902002107-main.pdf.txtExtracted texttext/plain41889https://repositorio.ufba.br/bitstream/ri/7324/3/1-s2.0-S0304414902002107-main.pdf.txt9abcec73e3dd2f3af077b7a72da7fef8MD53ri/73242022-07-05 14:03:22.428oai:repositorio.ufba.br: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Repositório InstitucionalPUBhttp://192.188.11.11:8080/oai/requestopendoar:19322022-07-05T17:03:22Repositório Institucional da UFBA - Universidade Federal da Bahia (UFBA)false
dc.title.pt_BR.fl_str_mv Time fuctuations of the random average process with parabolic initial conditions
dc.title.alternative.pt_BR.fl_str_mv Stochastic Processes and their Applications
title Time fuctuations of the random average process with parabolic initial conditions
spellingShingle Time fuctuations of the random average process with parabolic initial conditions
Fontes, L.R.G.
Random average process
Random surfaces
Harness process
Linear process
Surface !uctuations
Central limit theorem
title_short Time fuctuations of the random average process with parabolic initial conditions
title_full Time fuctuations of the random average process with parabolic initial conditions
title_fullStr Time fuctuations of the random average process with parabolic initial conditions
title_full_unstemmed Time fuctuations of the random average process with parabolic initial conditions
title_sort Time fuctuations of the random average process with parabolic initial conditions
author Fontes, L.R.G.
author_facet Fontes, L.R.G.
Medeiros, D.P.
Vachkovskaia, M.
author_role author
author2 Medeiros, D.P.
Vachkovskaia, M.
author2_role author
author
dc.contributor.author.fl_str_mv Fontes, L.R.G.
Medeiros, D.P.
Vachkovskaia, M.
Fontes, L.R.G.
Medeiros, D.P.
Vachkovskaia, M.
dc.subject.por.fl_str_mv Random average process
Random surfaces
Harness process
Linear process
Surface !uctuations
Central limit theorem
topic Random average process
Random surfaces
Harness process
Linear process
Surface !uctuations
Central limit theorem
description p. 257-276
publishDate 2003
dc.date.issued.fl_str_mv 2003
dc.date.accessioned.fl_str_mv 2012-12-07T15:30:52Z
dc.date.available.fl_str_mv 2012-12-07T15:30:52Z
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://www.repositorio.ufba.br/ri/handle/ri/7324
dc.identifier.issn.none.fl_str_mv 0304-4149
dc.identifier.number.pt_BR.fl_str_mv v. 103, n. 2
identifier_str_mv 0304-4149
v. 103, n. 2
url http://www.repositorio.ufba.br/ri/handle/ri/7324
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.pt_BR.fl_str_mv http://dx.doi.org/10.1016/S0304-4149(02)00210-7
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFBA
instname:Universidade Federal da Bahia (UFBA)
instacron:UFBA
instname_str Universidade Federal da Bahia (UFBA)
instacron_str UFBA
institution UFBA
reponame_str Repositório Institucional da UFBA
collection Repositório Institucional da UFBA
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