A Local Barycentric Version of the Bak–Sneppen Model
Kennerberg, Philip LU and Volkov, Stanislav LU
(2021)
In Journal of Statistical Physics
182(2).
- Abstract
We study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let N≥ 3 vertices be placed on a circle, such that each vertex has exactly two neighbours. To each vertex assign a real number, called fitness (we use this term, as it is quite standard for Bak–Sneppen models). Now find the vertex which fitness deviates most from the average of the fitnesses of its two immediate neighbours (in case of a tie, draw uniformly among such vertices), and replace it by a random value drawn independently according to some distribution ζ. We show that in case where ζ is a finitely supported or continuous uniform distribution, all... (More)
We study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let N≥ 3 vertices be placed on a circle, such that each vertex has exactly two neighbours. To each vertex assign a real number, called fitness (we use this term, as it is quite standard for Bak–Sneppen models). Now find the vertex which fitness deviates most from the average of the fitnesses of its two immediate neighbours (in case of a tie, draw uniformly among such vertices), and replace it by a random value drawn independently according to some distribution ζ. We show that in case where ζ is a finitely supported or continuous uniform distribution, all the fitnesses except one converge to the same value.
(Less)
- author
- Kennerberg, Philip
LU
and Volkov, Stanislav
LU
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bak–Sneppen model, Interacting particle systems, Jante’s law process
- in
- Journal of Statistical Physics
- volume
- 182
- issue
- 2
- article number
- 42
- publisher
- Springer
- external identifiers
-
- scopus:85100927192
- ISSN
- 0022-4715
- DOI
- 10.1007/s10955-021-02718-0
- language
- English
- LU publication?
- yes
- id
- 07d62aa8-3c2d-4ebb-9c3b-9378cbf81b06
- date added to LUP
- 2021-03-02 08:16:04
- date last changed
- 2022-04-27 00:27:38
@article{07d62aa8-3c2d-4ebb-9c3b-9378cbf81b06,
abstract = {{<p>We study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let N≥ 3 vertices be placed on a circle, such that each vertex has exactly two neighbours. To each vertex assign a real number, called fitness (we use this term, as it is quite standard for Bak–Sneppen models). Now find the vertex which fitness deviates most from the average of the fitnesses of its two immediate neighbours (in case of a tie, draw uniformly among such vertices), and replace it by a random value drawn independently according to some distribution ζ. We show that in case where ζ is a finitely supported or continuous uniform distribution, all the fitnesses except one converge to the same value.</p>}},
author = {{Kennerberg, Philip and Volkov, Stanislav}},
issn = {{0022-4715}},
keywords = {{Bak–Sneppen model; Interacting particle systems; Jante’s law process}},
language = {{eng}},
number = {{2}},
publisher = {{Springer}},
series = {{Journal of Statistical Physics}},
title = {{A Local Barycentric Version of the Bak–Sneppen Model}},
url = {{http://dx.doi.org/10.1007/s10955-021-02718-0}},
doi = {{10.1007/s10955-021-02718-0}},
volume = {{182}},
year = {{2021}},
}