Real roots of hypergeometric polynomials via finite free convolution
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913338511851520 |
|---|---|
| author | Martinez-Finkelshtein, Andrei Morales, Rafael Perales, Daniel |
| author_facet | Martinez-Finkelshtein, Andrei Morales, Rafael Perales, Daniel |
| contents | We examine two binary operations on the set of algebraic polynomials, known as multiplicative and additive finite free convolutions, specifically in the context of hypergeometric polynomials. We show that the representation of a hypergeometric polynomial as a finite free convolution of more elementary blocks, combined with the preservation of the real zeros and interlacing by the free convolutions, is an effective tool that allows us to analyze when all roots of a specific hypergeometric polynomial are real. Moreover, the known limit behavior of finite free convolutions allows us to write the asymptotic zero distribution of some hypergeometric polynomials as free convolutions of Marchenko-Pastur, reversed Marchenko-Pastur, and free beta laws, which has an independent interest within free probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10970 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Real roots of hypergeometric polynomials via finite free convolution Martinez-Finkelshtein, Andrei Morales, Rafael Perales, Daniel Classical Analysis and ODEs Probability 33C20, 33C45, 42C05, 46L54 We examine two binary operations on the set of algebraic polynomials, known as multiplicative and additive finite free convolutions, specifically in the context of hypergeometric polynomials. We show that the representation of a hypergeometric polynomial as a finite free convolution of more elementary blocks, combined with the preservation of the real zeros and interlacing by the free convolutions, is an effective tool that allows us to analyze when all roots of a specific hypergeometric polynomial are real. Moreover, the known limit behavior of finite free convolutions allows us to write the asymptotic zero distribution of some hypergeometric polynomials as free convolutions of Marchenko-Pastur, reversed Marchenko-Pastur, and free beta laws, which has an independent interest within free probability. |
| title | Real roots of hypergeometric polynomials via finite free convolution |
| topic | Classical Analysis and ODEs Probability 33C20, 33C45, 42C05, 46L54 |
| url | https://arxiv.org/abs/2309.10970 |