{"paper":{"title":"On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Its, Igor Krasovsky, Percy Deift, Thomas Bothner","submitted_at":"2014-07-10T19:19:54Z","abstract_excerpt":"We study the determinant $\\det(I-\\gamma K_s), 0<\\gamma <1$, of the integrable Fredholm operator $K_s$ acting on the interval $(-1,1)$ with kernel $K_s(\\lambda, \\mu)= \\frac{\\sin s(\\lambda - \\mu)}{\\pi (\\lambda-\\mu)}$. This determinant arises in the analysis of a log-gas of interacting particles in the bulk-scaling limit, at inverse temperature $\\beta=2$, in the presence of an external potential $v=-\\frac{1}{2}\\ln(1-\\gamma)$ supported on an interval of length $\\frac{2s}{\\pi}$. We evaluate, in particular, the double scaling limit of $\\det(I-\\gamma K_s)$ as $s\\rightarrow\\infty$ and $\\gamma\\uparrow "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2910","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"}