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  • 1907.03717v1

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Coexistence in a random growth model with competition

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
Article number26
<mark>Journal publication date</mark>27/03/2020
<mark>Journal</mark>Electronic Communications in Probability
Volume25
Number of pages14
Pages (from-to)1-14
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

14 Pages, 1 figure