{"paper":{"title":"Biorthogonal ensembles with two-particle interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.MP"],"primary_cat":"math-ph","authors_text":"Stefano Romano, Tom Claeys","submitted_at":"2013-12-10T17:37:13Z","abstract_excerpt":"We investigate determinantal point processes on $[0,+\\infty)$ of the form \\begin{equation*}\\label{probability distribution} \\frac{1}{Z_n}\\prod_{1\\leq i<j\\leq n}(\\lambda_j-\\lambda_i)\\prod_{1\\leq i<j\\leq n}(\\lambda_j^\\theta-\\lambda_i^\\theta) \\prod_{j=1}^n w(\\lambda_j)d\\lambda_j,\\qquad \\theta\\geq 1. \\end{equation*} We prove that the biorthogonal polynomials associated to such models satisfy a recurrence relation and a Christoffel-Darboux formula if $\\theta\\in\\mathbb Q$, and that they can be characterized in terms of $1\\times 2$ vector-valued Riemann-Hilbert problems which exhibit some non-standar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2892","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"}