A Local Barycentric Version of the Bak–Sneppen Model

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A Local Barycentric Version of the Bak–Sneppen Model. / Kennerberg, Philip; Volkov, Stanislav.

In: Journal of Statistical Physics, Vol. 182, No. 2, 42, 2021.

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TY - JOUR

T1 - A Local Barycentric Version of the Bak–Sneppen Model

AU - Kennerberg, Philip

AU - Volkov, Stanislav

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Bak–Sneppen model

KW - Interacting particle systems

KW - Jante’s law process

U2 - 10.1007/s10955-021-02718-0

DO - 10.1007/s10955-021-02718-0

M3 - Article

AN - SCOPUS:85100927192

VL - 182

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 1572-9613

IS - 2

M1 - 42

ER -