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arXiv · 2506.15500

On extinction and survival of the Bak-Sneppen model on arbitrary graphs

Serguei Popov·Stanislav Volkov
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Abstract

We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002) for a finite segment of $\mathbb{Z}^1$ with the periodic boundary condition to a large class of graphs, by using coupling between the Bak-Sneppen model and the oriented percolation in a quadrant. This allows us to avoid dealing with the so-called avalanches, thus simplifying many arguments.

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Serguei Popov, Stanislav Volkov. 2025-06-18. On extinction and survival of the Bak-Sneppen model on arbitrary graphs. https://arxiv.org/abs/2506.15500

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