Even Hypergeometric Polynomials and Finite Free Commutators
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918258119016448 |
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| author | Campbell, Jacob Morales, Rafael Perales, Daniel |
| author_facet | Campbell, Jacob Morales, Rafael Perales, Daniel |
| contents | We study in detail the class of even polynomials and their behavior with respect to finite free convolutions. To this end, we use some specific hypergeometric polynomials and a variation of the rectangular finite free convolution to understand even real-rooted polynomials in terms of positive-rooted polynomials. Then, we study some classes of even polynomials that are of interest in finite free probability, such as even hypergeometric polynomials, symmetrizations, and finite free commutators. Specifically, we provide many new examples of these objects, involving classical families of special polynomials (such as Laguerre, Hermite, and Jacobi). Finally, we relate the limiting root distributions of sequences of even polynomials with the corresponding symmetric measures that arise in free probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Even Hypergeometric Polynomials and Finite Free Commutators Campbell, Jacob Morales, Rafael Perales, Daniel Classical Analysis and ODEs Operator Algebras Probability 46L54, 33C20, 33C45 We study in detail the class of even polynomials and their behavior with respect to finite free convolutions. To this end, we use some specific hypergeometric polynomials and a variation of the rectangular finite free convolution to understand even real-rooted polynomials in terms of positive-rooted polynomials. Then, we study some classes of even polynomials that are of interest in finite free probability, such as even hypergeometric polynomials, symmetrizations, and finite free commutators. Specifically, we provide many new examples of these objects, involving classical families of special polynomials (such as Laguerre, Hermite, and Jacobi). Finally, we relate the limiting root distributions of sequences of even polynomials with the corresponding symmetric measures that arise in free probability. |
| title | Even Hypergeometric Polynomials and Finite Free Commutators |
| topic | Classical Analysis and ODEs Operator Algebras Probability 46L54, 33C20, 33C45 |
| url | https://arxiv.org/abs/2502.00254 |