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We are interested in limiting, as $\\nu\\to0$, behaviour of distributions of"},"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":"1311.6793","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-26T20:10:20Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d3e416920e8daabd7e3122af27b93ca59e306a931b60e4b7c90457eea3933d46","abstract_canon_sha256":"fa2437ec497b80efdbfbd0061c85267da2667cb02e4bb0d67772cba4716ef06d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:46.704968Z","signature_b64":"wvqvjk8TPoWgwUfxucmVxqLQYWyGKfbTa1uu8nM2MZacyg/UcloGohL6kk/ZE+E+wNhIOsuHg22pLXh0qHSrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c9bca027e4d414344819a7814916b40da84241e440596f5935513b0266499c9","last_reissued_at":"2026-05-18T02:54:46.704539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:46.704539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resonant averaging for small solutions of stochastic NLS equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alberto Maiocchi, Sergei Kuksin","submitted_at":"2013-11-26T20:10:20Z","abstract_excerpt":"We consider the free linear Schr\\\"odinger equation on a torus $\\mathbb T^d$, perturbed by a hamiltonian nonlinearity, driven by a random force and damped by a linear damping: $$ u_t -i\\Delta u +i\\nu \\rho |u|^{2q_*}u = - \\nu f(-\\Delta) u + \\sqrt\\nu\\,\\frac{d}{d t}\\sum_{k\\in \\mathbb Z^d} b_l\\beta^k(t)e^{ik\\cdot x} \\ . $$ Here $u=u(t,x),\\ x\\in\\mathbb T^d$, $0<\\nu\\ll 1$, $q_*\\in\\mathbb N$, $f$ is a positive continuous function, $\\rho$ is a positive parameter and $\\beta^k(t)$ are standard independent complex Wiener processes. 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