Geodesic
Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Katsunori Fujie and Yuki Ueda},
     title = {Law of {Large} {Numbers} for {Roots} of {Finite} {Free} {Multiplicative} {Convolution} of {Polynomials}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a3/}
}
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Katsunori Fujie; Yuki Ueda. Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a3/

[1] Arizmendi O., Garza-Vargas J., Perales D., Finite free cumulants: multiplicative convolutions, genus expansion and infinitesimal distributions, arXiv: 2108.08489

[2] Bercovici H., Voiculescu D., “Free convolution of measures with unbounded support”, Indiana Univ. Math. J., 42 (1993), 733–773 | DOI

[3] Haagerup U., Möller S., “The law of large numbers for the free multiplicative convolution”, Operator Algebra and Dynamics, Springer Proc. Math. Stat., 58, Springer, Heidelberg, 2013, 157–186, arXiv: 1211.4457 | DOI

[4] Hardy G.H., Littlewood J.E., Pólya G., Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1952

[5] Lindsay J.M., Pata V., “Some weak laws of large numbers in noncommutative probability”, Math. Z., 226 (1997), 533–543 | DOI

[6] Marcus A.W., Polynomial convolutions and (finite) free probability, arXiv: 2108.07054

[7] Marcus A.W., Spielman D.A., Srivastava N., “Finite free convolutions of polynomials”, Probab. Theory Related Fields, 182 (2022), 807–848, arXiv: 1504.00350 | DOI

[8] Tucci G.H., “Limits laws for geometric means of free random variables”, Indiana Univ. Math. J., 59 (2010), 1–13, arXiv: 0802.4226 | DOI

[9] Ueda Y., “Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution”, Bernoulli, 27 (2021), 502–531, arXiv: 2003.05382 | DOI

[10] Voiculescu D., “Multiplication of certain noncommuting random variables”, J. Operator Theory, 18 (1987), 223–235