Coexistence in a random growth model with competition

Turnbull, Shane and Turner, Amanda (2020) Coexistence in a random growth model with competition. Electronic Communications in Probability, 25: 26. pp. 1-14. ISSN 1083-589X

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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.

Item Type:

Journal Article

Journal or Publication Title:

Electronic Communications in Probability

Additional Information:

14 Pages, 1 figure

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2613

Subjects:

?? math.pr60fxx, 60k35random growth modelshastings-levitovscaling limitsergodic limitsstatistics and probabilitystatistics, probability and uncertainty ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

135634

Deposited By:

ep_importer_pure

Deposited On:

22 Jul 2019 09:10

Refereed?:

Yes

Published?:

Published

Last Modified:

30 Mar 2024 00:58

URI:

https://eprints.lancs.ac.uk/id/eprint/135634