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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A one-dimensional version of the random interlacements

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Author(s):
Camargo, Darcy [1] ; Popov, Serguei [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas, UNICAMP, Dept Stat, Inst Math Stat & Sci Computat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Stochastic Processes and their Applications; v. 128, n. 8, p. 2750-2778, AUG 2018.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 13/23081-6 - Percolation and random walks in dependent environments
Grantee:Darcy Gabriel Augusto de Camargo Cunha
Support Opportunities: Scholarships in Brazil - Doctorate (Direct)