{"paper":{"title":"Linear response for random dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Beno\\^it Saussol, Marks Ruziboev, Wael Bahsoun","submitted_at":"2017-10-10T16:26:11Z","abstract_excerpt":"We study for the first time linear response for random compositions of maps, chosen independently according to a distribution $\\PP$. We are interested in the following question: how does an absolutely continuous stationary measure (acsm) of a random system change when $\\PP$ changes smoothly to $\\PP_{\\eps}$? For a wide class of one dimensional random maps, we prove differentiability of acsm with respect to $\\eps$; moreover, we obtain a linear response formula. We apply our results to iid compositions, with respect to various distributions $\\PP_{\\eps}$, of uniformly expanding circle maps, Gauss-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03706","kind":"arxiv","version":2},"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"}