Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials

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dc.contributor.authorFujie, Katsunori
dc.contributor.authorUeda, Yuki
dc.date.accessioned2026-01-14T09:56:28Z
dc.date.issued2023
dc.description.abstractWe 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.
dc.description.sponsorshipThis 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.
dc.identifier.citationLaw of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials. Katsunori Fujie and Yuki Ueda. SIGMA 19 (2023), 004, 11 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2023.004
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 46L54; 26C10; 60F05
dc.identifier.otherarXiv:2208.11297
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211880
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleLaw of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2023, том 19, випуск за цей рік