{"paper":{"title":"Survival probability of stochastic processes beyond persistence exponents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. Dolgushev, N. Levernier, O. B\\'enichou, R. Voituriez, T. Gu\\'erin","submitted_at":"2019-07-08T14:11:01Z","abstract_excerpt":"For many stochastic processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\\sim S_0/t^\\theta$. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent $\\theta$ has been studied at length, the prefactor $S_0$, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for $S_0$ for a compact random walk in unbounded space by establishing an analytic relation with the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03632","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"}