THE BI-DIMENSIONAL DIRECTED IDLA FOREST

• 成果类型: Article
• 署名作者: Chenavier, Nicolas; Coupier, David; Rousselle, Arnaud
• 署名单位: Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1865
• 发表日期: 2023
• 页码: 2247-2290
• 关键词: diffusion-limited aggregation; 2d-directed spanning forest; stationary harmonic measure; internal dla; fluctuations; percolation; trees

摘要

We investigate three types of internal diffusion limited aggregation (IDLA) models. These models are based on simple random walks on Z2 with infinitely many sources that are the points of the vertical axis I (infinity) = {0}x Z. Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t. the hor-izontal direction) random forest spanning Z2, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations.