{"paper":{"title":"Pickands' constant at first order in an expansion around Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alberto Rosso, Kay J\\\"org Wiese, Mathieu Delorme","submitted_at":"2016-09-26T10:07:16Z","abstract_excerpt":"In the theory of extreme values of Gaussian processes, many results are expressed in terms of the Pickands constant $\\mathcal{H}_{\\alpha}$. This constant depends on the local self-similarity exponent $\\alpha$ of the process, i.e. locally it is a fractional Brownian motion (fBm) of Hurst index $H=\\alpha/2$. Despite its importance, only two values of the Pickands constant are known: ${\\cal H}_1 =1$ and ${\\cal H}_2=1/\\sqrt{\\pi}$. Here, we extend the recent perturbative approach to fBm to include drift terms. This allows us to investigate the Pickands constant $\\mathcal{H}_{\\alpha}$ around standar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07909","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"}