{"paper":{"title":"Super-diffusivity in a shear flow model from perpetual homogenization","license":"","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"G\\'erard Ben-Arous, Houman Owhadi","submitted_at":"2001-05-24T15:24:04Z","abstract_excerpt":"This paper is concerned with the asymptotic behavior solutions of stochastic differential equations $dy_t=d\\omega_t -\\nabla \\Gamma(y_t) dt$, $y_0=0$ and $d=2$. $\\Gamma$ is a $2\\times 2$ skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales $\\Gamma_{12}=-\\Gamma_{21}=h(x_1)$, with $h(x_1)=\\sum_{n=0}^\\infty \\gamma_n h^n(x_1/R_n)$ where $h^n$ are smooth functions of period 1, $h^n(0)=0$, $\\gamma_n$ and $R_n$ grow exponentially fast with $n$. We can show that $y_t$ has an anomalous fast behavior ($\\E[|y_t|^2]\\sim t^{1+\\nu}$ with $\\nu>0$) and obtain q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105199","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"}