{"paper":{"title":"Global fluctuations for 1D log-gas dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"J. Unterberger","submitted_at":"2016-07-04T07:59:28Z","abstract_excerpt":"We study in this article the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, \\begin{equation} d\\lambda_t^i=\\frac{1}{\\sqrt{N}} dW_t^i - V'(\\lambda_t^i) dt+ \\frac{\\beta}{2N} \\sum_{j\\not=i} \\frac{dt}{\\lambda^i_t-\\lambda^j_t}, \\qquad i=1,\\ldots,N, \\end{equation} with $\\beta>1$, sometimes called generalized Dyson's Brownian motion, describing the dissipative dynamics of a log-gas of $N$ equal charges with equilibrium measure corresponding to a $\\beta$-ensemble, with sufficiently regular convex potential $V$. The limit $N\\to\\infty$ is known to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00760","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"}