DIFFUSION LIMITED AGGREGATION ON THE BOOLEAN LATTICE
成果类型：
Article
署名作者：
Frieze, Alan; Pegden, Wesley
署名单位：
Carnegie Mellon University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/18-AAP1392
发表日期：
2018
页码：
3528-3557
关键词：
摘要：
In the Diffusion Limited Aggregation (DLA) process on Z(2), or more generally Z(d), particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a fractal with dimension strictly less than d. Very little has been shown rigorously about the process, however. We study an analogous process on the Boolean lattice {0, 1}(n), in which particles take random decreasing walks from (1, ... , 1), and stick at the last vertex before they encounter an occupied site for the first time; the vertex (0, ... , 0) is initially occupied. In this model, we can rigorously prove that lower levels of the lattice become full, and that the process ends by producing an isolated path of unbounded length reaching (1, ... , 1).
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