{"paper":{"title":"Dissipation and high disorder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Kunwoo Kim, Le Chen, Michael Cranston","submitted_at":"2014-11-24T20:46:45Z","abstract_excerpt":"Given a field $\\{B(x)\\}_{x\\in\\mathbf{Z}^d}$ of independent standard Brownian motions, indexed by $\\mathbf{Z}^d$, the generator of a suitable Markov process on $\\mathbf{Z}^d,\\,\\,\\mathcal{G},$ and sufficiently nice function $\\sigma:[0,\\infty)\\to[0,\\infty),$ we consider the influence of the parameter $\\lambda$ on the behavior of the system, \\begin{align*}\n  \\rm{d} u_t(x) = & (\\mathcal{G}u_t)(x)\\,\\rm{d} t + \\lambda\\sigma(u_t(x))\\rm{d} B_t(x)\n  \\qquad[t>0,\\ x\\in\\mathbf{Z}^d],\n  &u_0(x)=c_0\\delta_0(x). \\end{align*}\n  We show that for any $\\lambda>0$ in dimensions one and two the total mass $\\sum_{x\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6607","kind":"arxiv","version":1},"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"}