{"paper":{"title":"Finite Free Convolution: Infinitesimal Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.OA","math.SP"],"primary_cat":"math.PR","authors_text":"Daniel Perales (Notre Dame), Josue Vazquez-Becerra (CIMAT), Octavio Arizmendi (CIMAT)","submitted_at":"2025-05-03T05:53:06Z","abstract_excerpt":"Finite-free additive and multiplicative convolutions are operations on the set of polynomials with real roots, introduced independently by Szeg\\\"{o} and Walsh in the 1920s. These operations have regained some interest, in the last decade, after being rediscovered by Marcus, Spielman, and Srivastava as the expected characteristic polynomial of randomly rotated matrices. They converge, as the degree $d$ of the polynomials increases, to the additive and multiplicative convolution of measures from free probability of Voiculescu. In this paper, we investigate the fluctuations of order $1/d$ -- also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01705","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/2505.01705/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"}