{"paper":{"title":"Random Partitions and the Quantum Benjamin-Ono Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR","math.RT","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Moll","submitted_at":"2015-08-12T20:39:57Z","abstract_excerpt":"We derive exact and asymptotic results for random partitions from general results in the semi-classical analysis of coherent states applied to the classical periodic Benjamin-Ono equation at critical regularity $s= -1/2$. We find classical $dF_{\\star |v} (c| \\overline{\\varepsilon})$ and quantum $d\\hat{F}^{\\eta_{NS}}( c | \\hbar, \\overline{\\varepsilon})|_{\\Psi}$ conserved densities for this system with dispersion coefficient $\\overline{\\varepsilon}$ extending Nazarov-Sklyanin (2013). For quantum stationary states, this conserved density is $dF_{\\lambda}(c | \\varepsilon_2, \\varepsilon_1)$ the Ray"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03063","kind":"arxiv","version":3},"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"}