{"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-study-of-the-probability-distribution-of","title":"A Study of the Probability Distribution of the Balls in Bins Process with Power Law Feedback","arxiv_id":"2308.10734","date":"2023-08-21","proceeding":null,"authors":["Samuel Forbes"],"abstract":"We analyse the balls in bins process with feedback with primary focus on the power law feedback function $f(\\omega)=\\eta \\omega^{\\gamma}\\,$, $\\eta>0\\,$ $\\gamma \\geq0\\,$. Using the recursive solution to the master equation we find for power law feedback numerical evidence that the probability mass function for finite time scales asymptotically with $\\omega^{-\\gamma}\\,$ for $\\gamma>1\\,$. We also provide simulations supporting a previous result by Oliveira (corollary to Theorem 4 in \\cite{oliveira2009onset}) that the tail of the losers scale as $\\omega^{-(\\gamma-1)}\\,$ but extending to $N \\geq 2$ bins. We thus find evidence that the balls in bins process with power law feedback produces power law distributions as is common to many real world phenomena.","url_abs":"https://arxiv.org/abs/2308.10734v1","url_pdf":"https://arxiv.org/pdf/2308.10734v1.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-study-of-the-probability-distribution-of","repo_url":"https://github.com/saf92/urn-balls-in-bins-model","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}