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Oil and water : a two-type internal aggregation model
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Candellero, Elisabetta, Ganguly, Shirshendu, Hoffman, Christopher and Levine, Lionel (2017) Oil and water : a two-type internal aggregation model. Annals of Probability, 45 (6A). pp. 4019-4070. doi:10.1214/16-AOP1157
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Official URL: http://doi.org/10.1214/16-AOP1157
Abstract
We introduce a two-type internal DLA model which is an example of a non-unary 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.
| Item Type: | Journal Article | |||||||||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science > Statistics | |||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Probabilities, Abelian groups, Logarithms | |||||||||||||||||||||||||||
| Journal or Publication Title: | Annals of Probability | |||||||||||||||||||||||||||
| Publisher: | Institute of Mathematical Statistics | |||||||||||||||||||||||||||
| ISSN: | 0091-1798 | |||||||||||||||||||||||||||
| Official Date: | 27 November 2017 | |||||||||||||||||||||||||||
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| Volume: | 45 | |||||||||||||||||||||||||||
| Number: | 6A | |||||||||||||||||||||||||||
| Page Range: | pp. 4019-4070 | |||||||||||||||||||||||||||
| DOI: | 10.1214/16-AOP1157 | |||||||||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||||||||
| Funder: | United States. National Security Agency (USNSA) | |||||||||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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