{"paper":{"title":"The longest excursion of stochastic processes in nonequilibrium systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Claude Godreche, Gregory Schehr, Satya N. Majumdar","submitted_at":"2009-03-19T20:19:15Z","abstract_excerpt":"We consider the excursions, i.e. the intervals between consecutive zeros, of stochastic processes that arise in a variety of nonequilibrium systems and study the temporal growth of the longest one l_{\\max}(t) up to time t. For smooth processes, we find a universal linear growth < l_{\\max}(t) > \\simeq Q_{\\infty} t with a model dependent amplitude Q_\\infty. In contrast, for non-smooth processes with a persistence exponent \\theta, we show that < l_{\\max}(t) > has a linear growth if \\theta < \\theta_c while < l_{\\max}(t) > \\sim t^{1-\\psi} if \\theta > \\theta_c. The amplitude Q_{\\infty} and the expon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3414","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"}