A Local Barycentric Version of the Bak–Sneppen Model

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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 the fitnesses except one converge to the same value.

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Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • Bak–Sneppen model, Interacting particle systems, Jante’s law process
Original languageEnglish
Article number42
JournalJournal of Statistical Physics
Volume182
Issue number2
Publication statusPublished - 2021
Publication categoryResearch
Peer-reviewedYes