Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials
We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials that have only non-negative real roots. Moreover, we study the empirical root distributions of limit polynomials obtained through the law of large numbers of finite free multiplicative convolution...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211880 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials. Katsunori Fujie and Yuki Ueda. SIGMA 19 (2023), 004, 11 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862538619874443264 |
|---|---|
| author | Fujie, Katsunori Ueda, Yuki |
| author_facet | Fujie, Katsunori Ueda, Yuki |
| citation_txt | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials. Katsunori Fujie and Yuki Ueda. SIGMA 19 (2023), 004, 11 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials that have only non-negative real roots. Moreover, we study the empirical root distributions of limit polynomials obtained through the law of large numbers of finite free multiplicative convolution when their degree tends to infinity.
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| first_indexed | 2026-03-12T18:26:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211880 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T18:26:22Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fujie, Katsunori Ueda, Yuki 2026-01-14T09:56:28Z 2023 Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials. Katsunori Fujie and Yuki Ueda. SIGMA 19 (2023), 004, 11 pages 1815-0659 2020 Mathematics Subject Classification: 46L54; 26C10; 60F05 arXiv:2208.11297 https://nasplib.isofts.kiev.ua/handle/123456789/211880 https://doi.org/10.3842/SIGMA.2023.004 We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials that have only non-negative real roots. Moreover, we study the empirical root distributions of limit polynomials obtained through the law of large numbers of finite free multiplicative convolution when their degree tends to infinity. This work was supported by JSPS Open Partnership Joint Research Projects JPJSBP120209921 and Bilateral Joint Research Projects (JSPS-MEAE-MESRI, JPJSBP120203202). Moreover, K.F. was supported by the Hokkaido University Ambitious Doctoral Fellowship (Information Science and AI). Y.U. was supported by JSPS Grant-in-Aid for Scientific Research (B) 19H01791 and also JSPS Grant-in-Aid for Young Scientists 17H04823 and 22K13925. Both authors would like to thank Nikhil Srivastava (UC Berkeley) for giving us a three-day lecture on finite free probability theory at Kyoto University. Both authors also thank Benoît Collins (Kyoto University) and Noriyoshi Sakuma (Nagoya City University) for introducing the discussion. Thanks to the lectures, the authors could start to study the LLN for finite free multiplicative convolution. Furthermore, the authors would also like to thank the referees who gave useful comments to improve this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials Article published earlier |
| spellingShingle | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials Fujie, Katsunori Ueda, Yuki |
| title | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials |
| title_full | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials |
| title_fullStr | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials |
| title_full_unstemmed | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials |
| title_short | Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials |
| title_sort | law of large numbers for roots of finite free multiplicative convolution of polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211880 |
| work_keys_str_mv | AT fujiekatsunori lawoflargenumbersforrootsoffinitefreemultiplicativeconvolutionofpolynomials AT uedayuki lawoflargenumbersforrootsoffinitefreemultiplicativeconvolutionofpolynomials |