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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0105199","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2001-05-24T15:24:04Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"ab5f6f84cdb7982adfb2444a68cd3a057e9b06ed1b28a5f15c77efb6459df86c","abstract_canon_sha256":"a26ca3447d17afc09be45a0de635a2dd377c8fc19e3aaec733630a6fc9cfd442"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:07.844620Z","signature_b64":"k9CO0NdwK7yU2G1AmNOtdrjAisdYhKe/+dAWUGbaawS5F7g0sMkMqROjLov3fPZ0T3+fehLFIxyA1hoaOjiFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ead1a2354abdf746532c677085ce78abd2ad19f32302e73669c1939eefee8208","last_reissued_at":"2026-05-18T01:09:07.844126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:07.844126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $n$. 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