Oil and water: A two-type internal aggregation model | Zendy

Elisabetta Candellero | Zendy; Shirshendu Ganguly | Zendy; Christopher Hoffman | Zendy; Lionel Levine | Zendy

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Oil and water: A two-type internal aggregation model

Author(s) -

Elisabetta Candellero,

Shirshendu Ganguly,

Christopher Hoffman,

Lionel Levine

Publication year - 2017

Publication title -

the annals of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.184

H-Index - 98

eISSN - 2168-894X

pISSN - 0091-1798

DOI - 10.1214/16-aop1157

Subject(s) - type (biology) , scaling , mathematics , particle (ecology) , order (exchange) , limit (mathematics) , statistical physics , combinatorics , geometry , mathematical analysis , physics , geology , paleontology , oceanography , finance , economics

We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting withn \oil" andn \water" particles at the origin, the particles diuse in Z according to the following rule: whenever some site x2 Z has at least 1 oil and at least 1 water particle present, it res 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.

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