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Coexistence in a random growth model with competition

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

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Coexistence in a random growth model with competition. / Turnbull, Shane; Turner, Amanda.
In: Electronic Communications in Probability, Vol. 25, 26, 27.03.2020, p. 1-14.

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

Harvard

Turnbull, S & Turner, A 2020, 'Coexistence in a random growth model with competition', Electronic Communications in Probability, vol. 25, 26, pp. 1-14. https://doi.org/10.1214/20-ECP304

APA

Turnbull, S., & Turner, A. (2020). Coexistence in a random growth model with competition. Electronic Communications in Probability, 25, 1-14. Article 26. https://doi.org/10.1214/20-ECP304

Vancouver

Turnbull S, Turner A. Coexistence in a random growth model with competition. Electronic Communications in Probability. 2020 Mar 27;25:1-14. 26. doi: 10.1214/20-ECP304

Author

Turnbull, Shane ; Turner, Amanda. / Coexistence in a random growth model with competition. In: Electronic Communications in Probability. 2020 ; Vol. 25. pp. 1-14.

Bibtex

@article{87d12bf5eeb844548303408624b682ce,
title = "Coexistence in a random growth model with competition",
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 = "math.PR, 60Fxx, 60K35, random growth models, Hastings-Levitov, scaling limits, ergodic limits",
author = "Shane Turnbull and Amanda Turner",
note = "14 Pages, 1 figure",
year = "2020",
month = mar,
day = "27",
doi = "10.1214/20-ECP304",
language = "English",
volume = "25",
pages = "1--14",
journal = "Electronic Communications in Probability",
issn = "1083-589X",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - Coexistence in a random growth model with competition

AU - Turnbull, Shane

AU - Turner, Amanda

N1 - 14 Pages, 1 figure

PY - 2020/3/27

Y1 - 2020/3/27

N2 - 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.

AB - 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.

KW - math.PR

KW - 60Fxx, 60K35

KW - random growth models

KW - Hastings-Levitov

KW - scaling limits

KW - ergodic limits

U2 - 10.1214/20-ECP304

DO - 10.1214/20-ECP304

M3 - Journal article

VL - 25

SP - 1

EP - 14

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

M1 - 26

ER -