2016/08/02 by Darcy Camargo, Camargo, Darcy, Serguei Popov +1
Mathematics · #60F05 #60G50 #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60F05 #msc:60G50 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1608.01016
32 pages
arxiv created 2016/08/02 · openalex publication_date 2016/08/02 · arxiv updated 2016/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin, which makes them transient. We also 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 for sites far from the origin and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements' local times.