{"paper":{"title":"Passive tracer in non-Markovian, Gaussian velocity field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tymoteusz Chojecki","submitted_at":"2018-02-09T12:01:13Z","abstract_excerpt":"We consider the trajectory of a tracer that is the solution of an ordinary differential equation $\\dot\\bbX(t)=\\bbV(t, \\bbX(t)),\\ X(0)=0$, with the right hand side, that is a stationary, zero-mean, Gaussian vector field with incompressible realizations. It is known, see [K-F;C-X;K-L-O], that $\\bbX(t)/\\sqrt{t}$ converges in law, as $t\\to+\\infty$, to a normal, zero mean vector, provided that the field $V(t,x)$ is Markovian and has the spectral gap property. We wish to extend this result to the case when the field is not Markovian and its covariance matrix is given by a completely monotone Bernste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03215","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"}