{"paper":{"title":"Asymptotic Results of a Multiple-entry Reinforcement Process","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Caio Alves, Daniel Valesin, Rodrigo Ribeiro","submitted_at":"2019-08-27T15:07:53Z","abstract_excerpt":"We introduce a class of stochastic processes with reinforcement consisting of a sequence of random partitions $\\{\\mathcal{P}_t\\}_{t \\ge 1}$, where $\\mathcal{P}_t$ is a partition of $\\{1,2,\\dots, Rt\\}$. At each time~$t$,~$R$ numbers are added to the set being partitioned; of these, a random subset (chosen according to a time-dependent probability distribution) joins existing blocks, and the others each start new blocks on their own. Those joining existing blocks each choose a block with probability proportional to that block's cardinality, independently. We prove results concerning the asymptot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10260","kind":"arxiv","version":2},"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/1908.10260/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"}