{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-new-estimate-of-the-cutoff-value-in-the-bak","title":"A New Estimate of the Cutoff Value in the Bak-Sneppen Model","arxiv_id":"2111.10473","date":"2021-11-19","proceeding":null,"authors":["C. A. Fish","J. J. P. Veerman"],"abstract":"We present evidence that the Bak-Sneppen model of evolution on $N$ vertices requires $N^3$ iterates to reach equilibrium. This is substantially more than previous authors suggested (on the order of $N^2$). Based on that estimate, we present a novel algorithm inspired by previous rank-driven analyses of the model allowing for direct simulation of the model with populations of up to $N = 25600$ for $2\\cdot N^3$ iterations. These extensive simulations suggest a cutoff value of $x^* = 0.66692 \\pm 0.00003$, a value slightly lower than previously estimated yet still distinctly above $2/3$. We also study how the cutoff values $x^*_N$ at finite $N$ approximate the conjectured value $x^*$ at $N=\\infty$. Assuming $x^*_N-x^*_\\infty \\sim N^{-\\nu}$, we find that $\\nu=0.978\\pm 0.025$, which is significantly lower than previous estimates ($\\nu\\approx 1.4$).","url_abs":"https://arxiv.org/abs/2111.10473v3","url_pdf":"https://arxiv.org/pdf/2111.10473v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-new-estimate-of-the-cutoff-value-in-the-bak","repo_url":"https://github.com/camafish/bak-sneppen","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}