Bi-free extreme values

Huang, Hao-Wei; Wang, Jiun-Chau

doi:10.1016/j.jfa.2019.108392

Journal of Functional Analysis

2020

DOI: 10.1016/j.jfa.2019.108392

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Bi-free extreme values

Hao-Wei Huang

Jiun-Chau Wang

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2022

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“…We provide an application for domain of attractions in the context of free probability theory, see e.g. [2,3,10]. For, set k = 1.…”

mentioning

confidence: 99%

The maximum domain of attraction of multivariate extreme value distributions is small

Leonetti¹,

Chokami²

2022

Preprint

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Consider the set of Borel probability measures on R k and endow it with the topology of weak convergence. We show that the subset of all probability measures which belong to the domain of attraction of some multivariate extreme value distributions is dense and of the first Baire category. In addition, the analogue result holds in the context of free probability theory.for every bounded and continuous h : R k → R, see e.g. [4, Chapter 1].Let (X 1 , X 2 , . . .) be a sequence of i.i.d. random variables with values in R k . Let F ∈ P their common distribution, so that F (x) = Pr(X 1 ≤ x) for all x ∈ R k , where ≤ stands for the product pointwise order on R k . For each n ≥ 1, defineDefinition 1.1. We say that F belongs to the maximum domain of attraction, denoted by D, if there exist a sequence of functions (u 1 , u 2 , . . .

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“…We provide an application for domain of attractions in the context of free probability theory, see e.g. [2,3,10]. For, set k = 1.…”

mentioning

confidence: 99%

The maximum domain of attraction of multivariate extreme value distributions is small

Leonetti¹,

Chokami²

2022

Preprint

View full text Add to dashboard Cite

show abstract

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Bi-free extreme values

Cited by 1 publication

References 18 publications

The maximum domain of attraction of multivariate extreme value distributions is small

The maximum domain of attraction of multivariate extreme value distributions is small

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