INVASION PERCOLATION ON THE POISSON-WEIGHTED INFINITE TREE

• 成果类型: Article
• 署名作者: Addario-Berry, Louigi; Griffiths, Simon; Kang, Ross J.
• 署名单位: McGill University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Durham University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP761
• 发表日期: 2012
• 页码: 931-970
• 关键词: theorem

摘要

We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the sigma -> infinity limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420-466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it turns out that the two processes have extremely similar behavior. Finally, we introduce two new stationary representations of the Poisson incipient infinite cluster as random graphs on Z which are, in particular, factors of a homogeneous Poisson point process on the upper half-plane R x [0, infinity).