Coexistence in a random growth model with competition
| Autor: | Amanda Turner, Shane Turnbull |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
media_common.quotation_subject Probability (math.PR) Harmonic (mathematics) Growth model ergodic limits Harmonic measure scaling limits Competition (biology) Hastings-Levitov 60K35 random growth models Cluster (physics) FOS: Mathematics Ergodic theory Particle Limit (mathematics) Statistical physics Statistics Probability and Uncertainty 60Fxx 60K35 60Fxx Mathematics - Probability media_common Mathematics |
| Zdroj: | Electron. Commun. Probab. |
| DOI: | 10.48550/arxiv.1907.03717 |
| Popis: | 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. Comment: 14 Pages, 5 figures. Version 2 contains new figures including simulations, as well as some cosmetic changes |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|