On a Local Version of the Bak-Sneppen Model

Iddo Ben-Ari, Roger W C Silva

Published 2016-09-14Version 1

A major difficulty in studying the Bak-Sneppen model is to effectively couple or compare it with well-understood models. Motivated by this problem, we present a variant to Bak-Sneppen on finite connected graphs. The difference between our model and Bak-Sneppen is that instead of replacing the species in the neighborhood of the global fitness minimizer, we replace the species in a neighborhood of a properly defined local fitness minimizer. Our model is an ergodic Markov chain. We compute the stationary distribution and consider the limit when the number of the vertices tends to infinity. In particular, we show that for a sequence of regular graphs of constant degree, the fitness distribution under the stationary distribution converges to a product law.