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 \(N\ge 3\) 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 \(\zeta \). We show that in case where \(\zeta \) is a finitely supported or continuous uniform distribution, all the fitnesses except one converge to the same value.

我们研究了相互作用的粒子系统的行为，该行为与Kennerberg和Volkov中定义的Bak–Sneppen模型和Jante定律过程有关（Adv Appl Probab 50：414–439，2018）。让\（N \ ge 3 \）个顶点放置在一个圆上，以便每个顶点恰好有两个邻居。给每个顶点分配一个实数，称为适应度（我们使用此术语，因为它对于Bak–Sneppen模型是相当标准的）。现在找到适合度偏离其两个直接邻居的适合度平均值的顶点（如果是平局，则在这些顶点之间均匀绘制），然后将其替换为根据某个分布\（\ zeta \）。我们证明了在\（\ zeta \） 是有限支持的或连续的均匀分布，除一个以外的所有适应度都收敛到相同的值。