{"paper":{"title":"The Hausdorff measure of the boundary of the Brownian disk","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexis Metz--Donnadieu","submitted_at":"2024-11-25T16:25:06Z","abstract_excerpt":"Consider the boundary $\\partial \\mathbb D$ of the Brownian disk $\\mathbb D$ as a metric space by endowing it with the (restriction of the) metric of $\\mathbb D$. We show that the uniform measure on $\\partial \\mathbb D$ coincides with the Hausdorff measure associated with the gauge function $h(s)=\\kappa s^2\\log\\log(1/s)$ for some deterministic constant $\\kappa>0$. We also state the analogous result for the boundary of the Brownian half-plane $\\mathbb H$. This proves in particular that the uniform measure on the boundary of the Brownian disk (resp. the Brownian half-plane) is determined by the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16541","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/2411.16541/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"}