Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 004, 11 pages      arXiv:2208.11297

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

Katsunori Fujie a and Yuki Ueda b
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

Received August 25, 2022, in final form January 09, 2023; Published online January 14, 2023

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.

Key words: finite free probability; finite free multiplicative convolution; law of large numbers.

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