{"paper":{"title":"Multideterminantal measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Richard Kenyon","submitted_at":"2025-01-30T13:53:26Z","abstract_excerpt":"We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\\{1,2,\\dots,k\\}$, generalizing determinantal measures (which correspond to the case $k=2$). We give examples coming from the positive Grassmannian, from the dimer model and from the spanning tree model.\n  We characterize kernels of \\emph{pure} $k$-determinantal measures as those arising from $k$-tuples of Grassmannian elements whose maximal minors have certain sign restrictions. As a special case we construct all kernels of pure determinantal measures via a pair of elements of $Gr_{n_1,n}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18349","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.18349/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}