OIL AND WATER: A TWO-TYPE INTERNAL AGGREGATION MODEL

• 成果类型: Article
• 署名作者: Candellero, Elisabetta; Ganguly, Shirshendu; Hoffman, Christopher; Levine, Lionel
• 署名单位: University of Warwick; University of California System; University of California Berkeley; University of Washington; University of Washington Seattle; Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1157
• 发表日期: 2017
• 页码: 4019-4070
• 关键词: dla; fluctuations

摘要

We introduce a two-type internal DLA model which is an example of a nonunary abelian network. Starting with n oil and n water particles at the origin, the particles diffuse in Z according to the following rule: whenever some site x. Z has at least 1 oil and at least 1 water particle present, it fires by sending 1 oil particle and 1 water particle each to an independent random neighbor x +/- 1. Firing continues until every site has at most one type of particles. We establish the correct order for several statistics of this model and identify the scaling limit under assumption of existence.