{"paper":{"title":"Transformations of polynomial ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Arno B.J. Kuijlaars","submitted_at":"2015-01-22T14:23:51Z","abstract_excerpt":"A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\\frac{1}{Z_n} \\, \\prod_{j<k} (x_k-x_j) \\, \\det \\left[ f_k (x_j) \\right]_{j,k=1}^n$, for certain functions $f_1, \\ldots, f_n$. Such ensembles appear frequently as the joint eigenvalue density of random matrices. We present a number of transformations that preserve the structure of a polynomial ensemble. These transformations include the restriction of a Hermitian matrix by removing one row and one column, a rank-one modification of a Hermitian matrix, and the extension of a Hermitian matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05506","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"}