Final published version, 173 KB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -