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Under mild conditions, we prove that the preceding stochastic PDE has a unique solution that grows at most exponentially in time. And that, under natural conditions, it is \"weakly intermittent.\" Along the way, we establish a comparison principl"},"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":"0811.0643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-05T04:09:43Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"88588b0fdd0fe8105148467c3d39b32c78fd49d9f4bab67412bb68a6df7a9aee","abstract_canon_sha256":"e0c751c0a1bfe870573b051266d5f2e39cdb1aaaea8affdb14ce8cef1be40bd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:46.081281Z","signature_b64":"HYyj9V3uo3jh9N0pDTyQv43mKVqWTGlIoyH5GUuT2CEpgiMbjlP6uCQsW1TiLFsAJoBDeW0oHwG3eZnanQo1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c815a7c39df9eeb20774afb9e66c545e345f9db7161321065e86cce34cf1b3b6","last_reissued_at":"2026-05-18T03:49:46.080558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:46.080558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An asymptotic theory for randomly forced discrete nonlinear heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Mohammud Foondun","submitted_at":"2008-11-05T04:09:43Z","abstract_excerpt":"We study discrete nonlinear parabolic stochastic heat equations of the form, $u_{n+1}(x)-u_n(x)=(\\mathcal {L}u_n)(x)+\\sigma(u_n(x))\\xi_n(x)$, for $n\\in {\\mathbf{Z}}_+$ and $x\\in {\\mathbf{Z}}^d$, where $\\boldsymbol \\xi:=\\{\\xi_n(x)\\}_{n\\ge 0,x\\in {\\mathbf{Z}}^d}$ denotes random forcing and $\\mathcal {L}$ the generator of a random walk on ${\\mathbf{Z}}^d$. 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