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

Autor(es)

Popov, Serguei ^{[1, 2]} ; Rolla, Leonardo T. ^{[3, 4]} ; Ungaretti, Daniel ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, UNICAMP, Inst Math Stat & Sci Computat, Dept Stat, Rua Sergio Buarque Holanda 651, Campinas, SP - Brazil

^[2] Univ Porto, Ctr Matemat, CMUP, Rua Campo Alegre 687, Porto 4169007 - Portugal

^[3] Univ Buenos Aires, Argentina Natl Res Council, Buenos Aires, DF - Argentina

^[4] NYU Shanghai, NYU ECNU Inst Math Sci, Shanghai - Peoples R China

• Tipo de documento: Artigo Científico
• Fonte: ELECTRONIC JOURNAL OF PROBABILITY; v. 25, 2020.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 17/16294-4 - Percolação e entrelaçamentos aleatórios
• Beneficiário: Daniel Ungaretti Borges
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado