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{
    "pk": 64833,
    "title": "A rectangular additive convolution for polynomials",
    "subtitle": null,
    "abstract": "Motivated by the study of singular values of random rectangular matrices, we define and study the rectangular additive convolution of polynomials with nonnegative real roots. Our definition directly generalizes the asymmetric additive convolution introduced by Marcus, Spielman and Srivastava (2015), and our main theorem gives the corresponding generalization of the bound on the largest root from that paper. The main tool used in the analysis is a differential operator derived from the \"rectangular Cauchy transform\" introduced by Benaych-Georges (2009). The proof is inductive, with the base case requiring a new nonasymptotic bound on the Cauchy transform of Gegenbauer polynomials which may be of independent interest.\n \nMathematics Subject Classifications: 26C10, 33C45",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Polynomial convolutions"
        },
        {
            "word": "finite free probability"
        },
        {
            "word": "Gegenbauer polynomials"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/75t2b1bw",
    "frozenauthors": [
        {
            "first_name": "Aurelien",
            "middle_name": "",
            "last_name": "Gribinski",
            "name_suffix": "",
            "institution": "Princeton University, Princeton, New Jersey, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Adam",
            "middle_name": "W.",
            "last_name": "Marcus",
            "name_suffix": "",
            "institution": "École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T20:58:32Z",
    "date_accepted": "2022-03-23T20:58:32Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64833/galley/49643/download/"
        }
    ]
}