Homomorphisms relative to additive convolutions and max-convolutions: Free, boolean and classical cases

Ueda, Yuki

doi:10.1090/proc/15595

Proc. Amer. Math. Soc.

2021

DOI: 10.1090/proc/15595

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Homomorphisms relative to additive convolutions and max-convolutions: Free, boolean and classical cases

Yuki Ueda

Abstract: We introduce new homomorphisms relative to additive convolutions and max-convolutions in free, boolean and classical cases. Crucial roles are played by the limit distributions for free multiplicative law of large numbers.

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Rates of convergence for laws of the spectral maximum of free random variables

Ueda

2022

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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Let [Formula: see text] be a sequence of freely independent, identically distributed non-commutative random variables. Consider a sequence [Formula: see text] of the renormalized spectral maximum of random variables [Formula: see text]. It is known that the renormalized spectral maximum [Formula: see text] converges to the free extreme value distribution under certain conditions on the distribution function. In this paper, we provide a rate of convergence in the Kolmogorov distance between a distribution function of [Formula: see text] and the free extreme value distribution.

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Rates of convergence for laws of the spectral maximum of free random variables

Ueda

2022

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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Homomorphisms relative to additive convolutions and max-convolutions: Free, boolean and classical cases

Abstract: We introduce new homomorphisms relative to additive convolutions and max-convolutions in free, boolean and classical cases. Crucial roles are played by the limit distributions for free multiplicative law of large numbers.

Cited by 1 publication

References 29 publications

Rates of convergence for laws of the spectral maximum of free random variables

Rates of convergence for laws of the spectral maximum of free random variables

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