Oil and water: A two-type internal aggregation model

• Elisabetta Candellero ^[1] ; Shirshendu Ganguly ^[4] ; Christopher Hoffman ^[2] ; Lionel Levine ^[3]
  1. [1] University of Warwick

     University of Warwick

     Reino Unido

     
  2. [2] University of Washington

     University of Washington

     Estados Unidos

     
  3. [3] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
  4. [4] University of California (USA)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 1, 2017, págs. 4019-4070
• Idioma: inglés
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• Resumen

  • We introduce a two-type internal DLA model which is an example of a nonunary abelian network. Starting with nn “oil” and nn “water” particles at the origin, the particles diffuse in ZZ according to the following rule: whenever some site x∈Zx∈Z has at least 11 oil and at least 11 water particle present, it fires by sending 11 oil particle and 11 water particle each to an independent random neighbor x±1x±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.