{"paper":{"title":"On invariant Gibbs measures conditioned on mass and momentum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Jeremy Quastel, Tadahiro Oh","submitted_at":"2010-12-15T19:27:27Z","abstract_excerpt":"We construct a Gibbs measure for the nonlinear Schrodinger equation (NLS) on the circle, conditioned on prescribed mass and momentum: d \\mu_{a,b} = Z^{-1} 1_{\\int_T |u|^2 = a} 1_{i \\int_T u \\bar{u}_x = b} exp (\\pm1/p \\int_T |u|^p - 1/2 \\int_{\\T} |u|^2) d P for a \\in R^+ and b \\in R, where P is the complex-valued Wiener measure on the circle. We also show that \\mu_{a,b} is invariant under the flow of NLS. We note that i \\int_\\T u \\bar{u}_x is the Levy stochastic area, and in particular that this is invariant under the flow of NLS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3432","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"}