The fractional free convolution of $R$-diagonal elements and random polynomials under repeated differentiation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929276846080000 |
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| author | Campbell, Andrew O'Rourke, Sean Renfrew, David |
| author_facet | Campbell, Andrew O'Rourke, Sean Renfrew, David |
| contents | We extend the free convolution of Brown measures of $R$-diagonal elements introduced by Kösters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11935 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The fractional free convolution of $R$-diagonal elements and random polynomials under repeated differentiation Campbell, Andrew O'Rourke, Sean Renfrew, David Probability Operator Algebras We extend the free convolution of Brown measures of $R$-diagonal elements introduced by Kösters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions. |
| title | The fractional free convolution of $R$-diagonal elements and random polynomials under repeated differentiation |
| topic | Probability Operator Algebras |
| url | https://arxiv.org/abs/2307.11935 |