{"paper":{"title":"Shortest Path Lengths in Poisson Line Cox Processes: Approximations and Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT","stat.AP"],"primary_cat":"cs.IT","authors_text":"Gourab Ghatak, Martin Haenggi, Sanjoy Kumar Jhawar","submitted_at":"2024-11-25T14:44:15Z","abstract_excerpt":"We study street-constrained ($\\ell_1$) shortest paths in a Poisson line Cox process (PLCP), where Poisson points of linear intensity $\\mu$ lie on the lines of an underlying Poisson line process (PLP) of density $\\lambda$. Under a one-turn restriction, we derive closed-form expressions for the distribution of the nearest-neighbor path length from (i) the typical PLCP point and (ii) the typical PLP intersection, by explicitly evaluating the relevant void probabilities via a geometric decomposition of the feasible path-length set. For the intersection case, we further provide analytically tractab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16441","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/2411.16441/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"}