期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2018
卷号：XV
期号：2
页码：1065-1087
DOI：10.30757/ALEA.v15-39
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The extremal process of a branching random walk is the point measurerecording the position of particles alive at time n, shifted around the expectedposition of the minimal position. Madaule (2017) proved that this point measureconverges, as n → ∞, toward a randomly shifted, decorated Poisson point process.In this article, we study the joint convergence of the extremal process togetherwith its genealogical informations. This result is then used to describe the law ofthe decoration in the limiting process, as well as to study the supercritical Gibbsmeasures of the branching random walk.
关键词：Branching random walk; extremal process; decorated Poisson point;process; overlap probability;
