{"paper":{"title":"Mixing time of fractional random walk on finite fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR","math.NT"],"primary_cat":"math.PR","authors_text":"Huy Tuan Pham, Jimmy He, Max Wenqiang Xu","submitted_at":"2021-02-04T18:00:34Z","abstract_excerpt":"We study a random walk on $\\mathbb{F}_p$ defined by $X_{n+1}=1/X_n+\\varepsilon_{n+1}$ if $X_n\\neq 0$, and $X_{n+1}=\\varepsilon_{n+1}$ if $X_n=0$, where $\\varepsilon_{n+1}$ are independent and identically distributed. This can be seen as a non-linear analogue of the Chung--Diaconis--Graham process. We show that the mixing time is of order $\\log p$, answering a question of Chatterjee and Diaconis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.02781","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.02781/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}