{"paper":{"title":"From Random Walks to Random Leaps: Generalizing Classic Markov Chains for Big Data Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bala Rajaratnam, Doug Sparks, Meng-Hsuan Wu, Narut Sereewattanawoot","submitted_at":"2017-08-10T08:23:40Z","abstract_excerpt":"Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in which the allowed step sizes take values in the set $\\{\\pm1,\\pm2,\\ldots,\\pm k\\}$, a process we call a random leap. The need to analyze such models arises naturally in modern-day data science and so-called \"big data\" applications. We provide closed-form expressions for quantities associated with first passage times and absorption events of random leaps. These "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03116","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}