Even Hypergeometric Polynomials and Finite Free Commutators
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214191 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Even Hypergeometric Polynomials and Finite Free Commutators. Jacob Campbell, Rafael Morales and Daniel Perales. SIGMA 21 (2025), 108, 33 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580447384436736 |
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| author | Campbell, Jacob Morales, Rafael Perales, Daniel |
| author_facet | Campbell, Jacob Morales, Rafael Perales, Daniel |
| citation_txt | Even Hypergeometric Polynomials and Finite Free Commutators. Jacob Campbell, Rafael Morales and Daniel Perales. SIGMA 21 (2025), 108, 33 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 to the corresponding symmetric measures that arise in free probability.
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| first_indexed | 2026-03-21T12:21:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214191 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:21:55Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Campbell, Jacob Morales, Rafael Perales, Daniel 2026-02-20T07:59:44Z 2025 Even Hypergeometric Polynomials and Finite Free Commutators. Jacob Campbell, Rafael Morales and Daniel Perales. SIGMA 21 (2025), 108, 33 pages 1815-0659 2020 Mathematics Subject Classification: 46L54; 33C20; 33C45 arXiv:2502.00254 https://nasplib.isofts.kiev.ua/handle/123456789/214191 https://doi.org/10.3842/SIGMA.2025.108 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 to the corresponding symmetric measures that arise in free probability. This project originated during the 2023 Workshop in Analysis and Probability at Texas A&M University. We thank the organizers of the conferences YMC*A and IWOTA in August 2024, where two of the authors had fruitful discussions. We also thank Andrew Campbell for bringing some recent references to our attention. We greatly appreciate the corrections and useful suggestions offered by the anonymous referees. D.P. was partially supported by the AMS-Simons Travel Grant. The author also appreciates the hospitality of the University of Virginia during April 2024. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Even Hypergeometric Polynomials and Finite Free Commutators Article published earlier |
| spellingShingle | Even Hypergeometric Polynomials and Finite Free Commutators Campbell, Jacob Morales, Rafael Perales, Daniel |
| title | Even Hypergeometric Polynomials and Finite Free Commutators |
| title_full | Even Hypergeometric Polynomials and Finite Free Commutators |
| title_fullStr | Even Hypergeometric Polynomials and Finite Free Commutators |
| title_full_unstemmed | Even Hypergeometric Polynomials and Finite Free Commutators |
| title_short | Even Hypergeometric Polynomials and Finite Free Commutators |
| title_sort | even hypergeometric polynomials and finite free commutators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214191 |
| work_keys_str_mv | AT campbelljacob evenhypergeometricpolynomialsandfinitefreecommutators AT moralesrafael evenhypergeometricpolynomialsandfinitefreecommutators AT peralesdaniel evenhypergeometricpolynomialsandfinitefreecommutators |