ONE-DIMENSIONAL LONG-RANGE DIFFUSION-LIMITED AGGREGATION I

• 成果类型: Article
• 署名作者: Amir, Gideon; Angel, Omer; Benjamini, Itai; Kozma, Gady
• 署名单位: Bar Ilan University; University of British Columbia; Weizmann Institute of Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1058
• 发表日期: 2016
• 页码: 3546-3579
• 关键词: internal dla; percolation models; fluctuations; GROWTH; bounds; time

摘要

We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. Under various regularity conditions on the tail of the step distribution, we prove that the diameter grows as n(beta+o(1)), with an explicitly given beta. The growth rate of the aggregate is shown to have three phase transitions, when the walk steps have finite third moment, finite variance, and conjecturally, finite half moment.