A one-dimensional version of the random interlacements

Autor(es)

Camargo, Darcy ^[1] ; Popov, Serguei ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, UNICAMP, Dept Stat, Inst Math Stat & Sci Computat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Stochastic Processes and their Applications; v. 128, n. 8, p. 2750-2778, AUG 2018.
• Citações Web of Science: 0

Resumo

We base ourselves on the construction of the two-dimensional random interlacements (Comets et al., 2016) to define the one-dimensional version of the process. For this, we consider simple random walks conditioned on never hitting the origin. We compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements' local time and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements' local times. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 13/23081-6 - Percolação e passeios aleatórios em meios dependentes
• Beneficiário: Darcy Gabriel Augusto de Camargo Cunha
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto