{"paper":{"title":"On the convex hull of a planar Brownian bridge with a random Gaussian endpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luka \\v{S}imek, Nikola Sandri\\'c, Stjepan \\v{S}ebek","submitted_at":"2026-06-23T12:19:02Z","abstract_excerpt":"We consider a one-parameter family of isotropic planar Gaussian processes\n  \\[\n  X_\\sigma(t) =B_t+\\sigma t Z,\\qquad 0\\le t\\le 1,\\quad 0\\le \\sigma\\le 1,\n  \\]\n  where $B$ is a standard ($0$-to-$0$) planar Brownian bridge on $[0,1]$, and $Z\\sim \\mathrm N(0,I)$ is a standard Gaussian random vector independent of $B$. The family interpolates between standard planar Brownian bridge ($\\sigma=0$) and standard planar Brownian motion ($\\sigma=1$). As the main result of the paper we compute the expected perimeter and area of the convex hull of the random set $\\left\\{X_\\sigma(t) \\colon 0\\le t\\le 1\\right\\}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24485","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24485/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"}