{"paper":{"title":"Random Matrices with Merging Singularities and the Painlev\\'e V Equation","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CA","math.CV","math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin Fahs, Tom Claeys","submitted_at":"2015-08-27T07:15:00Z","abstract_excerpt":"We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form $\\frac{1}{Z_n} \\big|\\det \\big( M^2-tI \\big)\\big|^{\\alpha} e^{-n\\operatorname{Tr} V(M)}dM$, where $M$ is an $n\\times n$ Hermitian matrix, $\\alpha>-1/2$ and $t\\in\\mathbb R$, in double scaling limits where $n\\to\\infty$ and simultaneously $t\\to 0$. If $t$ is proportional to $1/n^2$, a transition takes place which can be described in terms of a family of solutions to the Painlev\\'e V equation. These Painlev\\'e solutions are in general transcendental functions, but for certain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06734","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"}