Competition on Zd driven by branching random walk
Deijfen, Maria and Vilkas, Timo LU
(2023)
In Electronic Communications in Probability
28.
- Abstract
A competition process on Zd is considered, where two species compete to color the sites. The entities are driven by branching random walks. Specifically red (blue) particles reproduce in discrete time and place offspring according to a given reproduction law, which may be different for the two types. When a red (blue) particle is placed at a site that has not been occupied by any particle before, the site is colored red (blue) and keeps this color forever. The types interact in that, when a particle is placed at a site of opposite color, the particle adopts the color of the site with probability p ∈ [0, 1]. Can a given type color infinitely many sites? Can both types color infinitely many sites simultaneously? Partial answers... (More)
A competition process on Zd is considered, where two species compete to color the sites. The entities are driven by branching random walks. Specifically red (blue) particles reproduce in discrete time and place offspring according to a given reproduction law, which may be different for the two types. When a red (blue) particle is placed at a site that has not been occupied by any particle before, the site is colored red (blue) and keeps this color forever. The types interact in that, when a particle is placed at a site of opposite color, the particle adopts the color of the site with probability p ∈ [0, 1]. Can a given type color infinitely many sites? Can both types color infinitely many sites simultaneously? Partial answers are given to these questions and many open problems are formulated.
(Less)
- author
- Deijfen, Maria
and Vilkas, Timo
LU
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- asymptotic shape, branching random walk, coexistence, competing growth
- in
- Electronic Communications in Probability
- volume
- 28
- article number
- 15
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- scopus:85152005566
- ISSN
- 1083-589X
- DOI
- 10.1214/23-ECP521
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2023, Institute of Mathematical Statistics. All rights reserved.
- id
- 212e7731-ee81-4cc0-bb8e-9efa7607cff9
- date added to LUP
- 2023-12-14 13:15:59
- date last changed
- 2023-12-14 15:04:19
@article{212e7731-ee81-4cc0-bb8e-9efa7607cff9,
abstract = {{<p>A competition process on Z<sup>d</sup> is considered, where two species compete to color the sites. The entities are driven by branching random walks. Specifically red (blue) particles reproduce in discrete time and place offspring according to a given reproduction law, which may be different for the two types. When a red (blue) particle is placed at a site that has not been occupied by any particle before, the site is colored red (blue) and keeps this color forever. The types interact in that, when a particle is placed at a site of opposite color, the particle adopts the color of the site with probability p ∈ [0, 1]. Can a given type color infinitely many sites? Can both types color infinitely many sites simultaneously? Partial answers are given to these questions and many open problems are formulated.</p>}},
author = {{Deijfen, Maria and Vilkas, Timo}},
issn = {{1083-589X}},
keywords = {{asymptotic shape; branching random walk; coexistence; competing growth}},
language = {{eng}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Electronic Communications in Probability}},
title = {{Competition on Z<sup>d</sup> driven by branching random walk}},
url = {{http://dx.doi.org/10.1214/23-ECP521}},
doi = {{10.1214/23-ECP521}},
volume = {{28}},
year = {{2023}},
}