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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 004, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.004 (Mi sigma1899) 		 
Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials

Katsunori Fujiea, Yuki Uedab

a Department of Mathematics, Hokkaido University, North 10 West 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan
b Department of Mathematics, Hokkaido University of Education, Hokumon-cho 9, Asahikawa, Hokkaido, 070-8621, Japan
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DOI: https://doi.org/10.3842/SIGMA.2023.004
Abstract: We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials which 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.
Keywords: finite free probability, finite free multiplicative convolution, law of large numbers.
Funding agency Grant number
Japan Society for the Promotion of Science JPJSBP120209921
JSPS-MEAE-MESRI
JPJSBP120203202
19H01791
17H04823
22K13925
Hokkaido University Ambitious Doctoral Fellowship
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.
Received: August 25, 2022; in final form January 9, 2023; Published online January 14, 2023
Bibliographic databases:
Document Type: Article
MSC: 46L54, 26C10, 60F05
Language: English
Citation: Katsunori Fujie, Yuki Ueda, “Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials”, SIGMA, 19 (2023), 004, 11 pp.
Citation in format AMSBIB
\Bibitem{FujUed23}
\by Katsunori~Fujie, Yuki~Ueda
\paper Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials
\jour SIGMA
\yr 2023
\vol 19
\papernumber 004
\totalpages 11
\mathnet{http://mi.mathnet.ru/sigma1899}
\crossref{https://doi.org/10.3842/SIGMA.2023.004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4533559}
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