{"paper":{"title":"Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Christophe Carr\\'e, Jean-Gabriel Luque, Matthieu Deneufchatel, Pierpaolo Vivo","submitted_at":"2010-03-31T09:20:55Z","abstract_excerpt":"We investigate the asymptotic behavior of the Selberg-like integral $$ \\frac1{N!}\\int_{[0,1]^N}x_1^p\\prod_{i<j}(x_i-x_j)^2\\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i$$, as $N\\to\\infty$ for different scalings of the parameters $a$ and $b$ with $N$. Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting $N$ channels in the two attached leads. Making use of Newton's interpolation formula, we show that an asymptotic limit exists and we compute it explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5996","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"}