Transience of conditioned walks on the plane: Encounters and speed of escape

Autores
Popov, Serguei; Trivellato Rolla, Leonardo; Ungaretti, Daniel
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is, formally speaking, the Doob’s h-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.
Fil: Popov, Serguei. Universidad de Porto; Portugal. Universidade Estadual de Campinas; Brasil
Fil: Trivellato Rolla, Leonardo. 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: Ungaretti, Daniel. Universidade Estadual de Campinas; Brasil
Materia
CONDITIONING
DOOB’S H-TRANSFORM
SIMPLE RANDOM WALK
TRANSIENCE
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:11336/143903
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Transience of conditioned walks on the plane: Encounters and speed of escapePopov, SergueiTrivellato Rolla, LeonardoUngaretti, DanielCONDITIONINGDOOB’S H-TRANSFORMSIMPLE RANDOM WALKTRANSIENCEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is, formally speaking, the Doob’s h-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.Fil: Popov, Serguei. Universidad de Porto; Portugal. Universidade Estadual de Campinas; BrasilFil: Trivellato Rolla, Leonardo. 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: Ungaretti, Daniel. Universidade Estadual de Campinas; BrasilProject Euclid2020-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143903Popov, Serguei; Trivellato Rolla, Leonardo; Ungaretti, Daniel; Transience of conditioned walks on the plane: Encounters and speed of escape; Project Euclid; Electronic Journal Of Probability; 25; 10-20201083-6489CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1214/20-EJP458info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Transience-of-conditioned-walks-on-the-plane--encounters-and/10.1214/20-EJP458.fullinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:25Zoai:ri.conicet.gov.ar:11336/143903instacron: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:34982025-10-22 11:54:26.091CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Transience of conditioned walks on the plane: Encounters and speed of escape
title Transience of conditioned walks on the plane: Encounters and speed of escape
spellingShingle Transience of conditioned walks on the plane: Encounters and speed of escape
Popov, Serguei
CONDITIONING
DOOB’S H-TRANSFORM
SIMPLE RANDOM WALK
TRANSIENCE
title_short Transience of conditioned walks on the plane: Encounters and speed of escape
title_full Transience of conditioned walks on the plane: Encounters and speed of escape
title_fullStr Transience of conditioned walks on the plane: Encounters and speed of escape
title_full_unstemmed Transience of conditioned walks on the plane: Encounters and speed of escape
title_sort Transience of conditioned walks on the plane: Encounters and speed of escape
dc.creator.none.fl_str_mv Popov, Serguei
Trivellato Rolla, Leonardo
Ungaretti, Daniel
author Popov, Serguei
author_facet Popov, Serguei
Trivellato Rolla, Leonardo
Ungaretti, Daniel
author_role author
author2 Trivellato Rolla, Leonardo
Ungaretti, Daniel
author2_role author
author
dc.subject.none.fl_str_mv CONDITIONING
DOOB’S H-TRANSFORM
SIMPLE RANDOM WALK
TRANSIENCE
topic CONDITIONING
DOOB’S H-TRANSFORM
SIMPLE RANDOM WALK
TRANSIENCE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is, formally speaking, the Doob’s h-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.
Fil: Popov, Serguei. Universidad de Porto; Portugal. Universidade Estadual de Campinas; Brasil
Fil: Trivellato Rolla, Leonardo. 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: Ungaretti, Daniel. Universidade Estadual de Campinas; Brasil
description We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is, formally speaking, the Doob’s h-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.
publishDate 2020
dc.date.none.fl_str_mv 2020-10
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/11336/143903
Popov, Serguei; Trivellato Rolla, Leonardo; Ungaretti, Daniel; Transience of conditioned walks on the plane: Encounters and speed of escape; Project Euclid; Electronic Journal Of Probability; 25; 10-2020
1083-6489
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143903
identifier_str_mv Popov, Serguei; Trivellato Rolla, Leonardo; Ungaretti, Daniel; Transience of conditioned walks on the plane: Encounters and speed of escape; Project Euclid; Electronic Journal Of Probability; 25; 10-2020
1083-6489
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1214/20-EJP458
info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Transience-of-conditioned-walks-on-the-plane--encounters-and/10.1214/20-EJP458.full
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
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/pdf
dc.publisher.none.fl_str_mv Project Euclid
publisher.none.fl_str_mv Project Euclid
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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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score 12.982451

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