{"paper":{"title":"Stationary states in single-well potentials under symmetric Levy noises","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Aleksei V. Chechkin, Bartlomiej Dybiec, Igor M. Sokolov","submitted_at":"2010-05-05T15:02:26Z","abstract_excerpt":"We discuss the existence of stationary states for subharmonic potentials  $V(x) \\propto |x|^c$, $c<2$, under action of symmetric $\\alpha$-stable noises. We show analytically that the necessary condition for the existence of the steady state is $c>2-\\alpha$. These states are characterized by heavy-tailed probability density functions which decay as $P(x) \\propto x^{-(c+\\alpha -1)}$ for $|x| \\to \\infty$, i.e. stationary states posses a heavier tail than the corresponding $\\alpha$-stable law. Monte Carlo simulations confirm the existence of such stationary states and the form of the tails of corr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0772","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"}