{"paper":{"title":"Renewal Structure of the Brownian Taut String","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer","submitted_at":"2015-09-24T12:39:49Z","abstract_excerpt":"In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time $T$.\n  In this note, we exhibit a natural renewal structure for the Brownian taut string, which is directly related to the time decomposition of the Brownian motion in terms of its $h$-extrema (as first introduced by Neveu and Pitman). Using this renewal structure, we de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07343","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"}