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2020 Coexistence in a random growth model with competition
Shane Turnbull, Amanda Turner
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP304


We consider a variation of the Hastings-Levitov model HL(0) for random growth in which the growing cluster consists of two competing regions. We allow the size of successive particles to depend both on the region in which the particle is attached, and the harmonic measure carried by that region. We identify conditions under which one can ensure coexistence of both regions. In particular, we consider whether it is possible for the process giving the relative harmonic measures of the regions to converge to a non-trivial ergodic limit.


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Shane Turnbull. Amanda Turner. "Coexistence in a random growth model with competition." Electron. Commun. Probab. 25 1 - 14, 2020.


Received: 7 July 2019; Accepted: 28 February 2020; Published: 2020
First available in Project Euclid: 27 March 2020

zbMATH: 1442.60105
MathSciNet: MR4089733
Digital Object Identifier: 10.1214/20-ECP304

Primary: 60Fxx , 60K35

Keywords: ergodic limits , Hastings-Levitov , random growth models , scaling limits


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