STATIONARY EDEN MODEL ON CAYLEY GRAPHS

• 成果类型: Article
• 署名作者: Antunovic, Tonci; Procaccia, Eviatar B.
• 署名单位: University of California System; University of California Los Angeles; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1210
• 发表日期: 2017
• 页码: 517-549
• 关键词: 1st passage percolation; directed polymers; diffusion

摘要

We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass transport principle, we generalize the result to Eden model in graphs of the form G x z(+), where G is a Cayley graph. This generalizes certain known results on the two-type Richardson model, in particular of Deijfen and Haggstrom in 2007 [Ann. Appl Probab. 17 (2007) 1639-1656].