English

Coexistence in a random growth model with competition

Probability 2020-04-03 v2

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.

Keywords

Cite

@article{arxiv.1907.03717,
  title  = {Coexistence in a random growth model with competition},
  author = {Shane Turnbull and Amanda Turner},
  journal= {arXiv preprint arXiv:1907.03717},
  year   = {2020}
}

Comments

14 Pages, 5 figures. Version 2 contains new figures including simulations, as well as some cosmetic changes

R2 v1 2026-06-23T10:15:05.688Z