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.

Detaljer

Författare
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Sannolikhetsteori och statistik

Nyckelord

Originalspråkengelska
Artikelnummer42
TidskriftJournal of Statistical Physics
Volym182
Utgåva nummer2
StatusPublished - 2021
PublikationskategoriForskning
Peer review utfördJa