{"paper":{"title":"The sine process under the influence of a varying potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Its, Igor Krasovsky, Percy Deift, Thomas Bothner","submitted_at":"2018-07-30T15:08:49Z","abstract_excerpt":"We review the authors' recent work \\cite{BDIK1,BDIK2,BDIK3} where we obtain the uniform large $s$ asymptotics for the Fredholm determinant $D(s,\\gamma):=\\det(I-\\gamma K_s\\upharpoonright_{L^2(-1,1)})$, $0\\leq\\gamma\\leq 1$. The operator $K_s$ acts with kernel $K_s(x,y)=\\sin(s(x-y))/(\\pi(x-y))$ and $D(s,\\gamma)$ appears for instance in Dyson's model \\cite{Dyson2} of a Coulomb log-gas with varying external potential or in the bulk scaling analysis of the thinned GUE \\cite{BP}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11387","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"}