{"paper":{"title":"Crystallization of random matrix orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"primary_cat":"math.PR","authors_text":"Adam W. Marcus, Vadim Gorin","submitted_at":"2017-06-22T16:46:56Z","abstract_excerpt":"Three operations on eigenvalues of real/complex/quaternion (corresponding to $\\beta=1,2,4$) matrices, obtained from cutting out principal corners, adding, and multiplying matrices can be extrapolated to general values of $\\beta>0$ through associated special functions.\n  We show that $\\beta\\to\\infty$ limit for these operations leads to the finite free projection, additive convolution, and multiplicative convolution, respectively.\n  The limit is the most transparent for cutting out the corners, where the joint distribution of the eigenvalues of principal corners of a uniformly-random general $\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07393","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"}