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November 2017 Oil and water: A two-type internal aggregation model
Elisabetta Candellero, Shirshendu Ganguly, Christopher Hoffman, Lionel Levine
Ann. Probab. 45(6A): 4019-4070 (November 2017). DOI: 10.1214/16-AOP1157


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 $\mathbb{Z}$ according to the following rule: whenever some site $x\in\mathbb{Z}$ 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 $x\pm1$. 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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Elisabetta Candellero. Shirshendu Ganguly. Christopher Hoffman. Lionel Levine. "Oil and water: A two-type internal aggregation model." Ann. Probab. 45 (6A) 4019 - 4070, November 2017.


Received: 1 August 2014; Revised: 1 May 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 06838114
MathSciNet: MR3729622
Digital Object Identifier: 10.1214/16-AOP1157

Primary: 60J10 , 60K35 , 82B41 , 82C22 , 82C24

Keywords: Internal DLA , nonunary abelian network , odometer function , Random walk , Scaling limit

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6A • November 2017
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