Distribution of the roots of Eulerian polynomials
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866911262873485312 |
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| author | Melotti, Paul |
| author_facet | Melotti, Paul |
| contents | We give a new proof that the empirical measures of the roots of Eulerian polynomials converge to a certain log-Cauchy distribution. To do so, we show that each moment of the roots of a related family of polynomials not only converge, but in fact become ultimately constant. These asymptotic moments are expressed in terms of Cauchy numbers of the second kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distribution of the roots of Eulerian polynomials Melotti, Paul Combinatorics Classical Analysis and ODEs Number Theory Probability We give a new proof that the empirical measures of the roots of Eulerian polynomials converge to a certain log-Cauchy distribution. To do so, we show that each moment of the roots of a related family of polynomials not only converge, but in fact become ultimately constant. These asymptotic moments are expressed in terms of Cauchy numbers of the second kind. |
| title | Distribution of the roots of Eulerian polynomials |
| topic | Combinatorics Classical Analysis and ODEs Number Theory Probability |
| url | https://arxiv.org/abs/2507.15908 |