{"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/mixing-time-of-pagerank-surfers-on-sparse","title":"Mixing time of PageRank surfers on sparse random digraphs","arxiv_id":"1905.04993","date":"2019-05-13","proceeding":null,"authors":["Pietro Caputo","Matteo Quattropani"],"abstract":"We consider the generalised PageRank walk on a digraph $G$, with refresh probability $\\alpha$ and resampling distribution $\\lambda$. We analyse convergence to stationarity when $G$ is a large sparse random digraph with given degree sequences, in the limit of vanishing $\\alpha$. We identify three scenarios: when $\\alpha$ is much smaller than the inverse of the mixing time of $G$ the relaxation to equilibrium is dominated by the simple random walk and displays a cutoff behaviour; when $\\alpha$ is much larger than the inverse of the mixing time of $G$ on the contrary one has pure exponential decay with rate $\\alpha$; when $\\alpha$ is comparable to the inverse of the mixing time of $G$ there is a mixed behaviour interpolating between cutoff and exponential decay. This trichotomy is shown to hold uniformly in the starting point and uniformly in the resampling distribution $\\lambda$.","url_abs":"https://arxiv.org/abs/1905.04993v3","url_pdf":"https://arxiv.org/pdf/1905.04993v3.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":"mixing-time-of-pagerank-surfers-on-sparse","repo_url":"https://github.com/newptcai/DCM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"mixing-time-of-pagerank-surfers-on-sparse","repo_url":"https://github.com/newptcai/DCM.wl","is_official":0,"mentioned_in_paper":0,"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}