{"paper":{"title":"Pathwise estimates for an effective dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frederic Legoll, Stefano Olla, Tony Lelievre","submitted_at":"2016-05-09T16:14:48Z","abstract_excerpt":"Starting from the overdamped Langevin dynamics in $\\mathbb{R}^n$, $$ dX_t = -\\nabla V(X_t) dt + \\sqrt{2 \\beta^{-1}} dW_t, $$ we consider a scalar Markov process $\\xi_t$ which approximates the dynamics of the first component $X^1_t$. In the previous work [F. Legoll, T. Lelievre, Nonlinearity 2010], the fact that $(\\xi_t)_{t \\ge 0}$ is a good approximation of $(X^1_t)_{t \\ge 0}$ is proven in terms of time marginals, under assumptions quantifying the timescale separation between the first component and the other components of $X_t$. Here, we prove an upper bound on the trajectorial error $\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02644","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"}