The expectation of the Vandermonde product squared for uniform random variables

Richard Ehrenborg

doi:10.1016/j.aam.2020.102030

The expectation of the Vandermonde product squared for uniform random variables

Richard Ehrenborg

Mathematics

Producción científica: Article › revisión exhaustiva

Resumen

Let X₁,X₂,…,X_n be independent random variables, each uniformly distributed on the interval (0,1). We compute the expectation of (X₁X₂⋯X_n)^k⋅∏_1≤i<j≤n(X_j−X_i)². The result relies on operators, the extended Vandermonde determinant and the hook formula for standard Young tableaux.

Idioma original	English
Número de artículo	102030
Publicación	Advances in Applied Mathematics
Volumen	118
DOI	https://doi.org/10.1016/j.aam.2020.102030
Estado	Published - jul 2020

Nota bibliográfica

Publisher Copyright:
© 2020 Elsevier Inc.

Financiación

The author thanks Theodore Ehrenborg for comments on an earlier draft of this paper. This work was supported by a grant from the Simons Foundation (# 429370 , Richard Ehrenborg).

Financiadores	Número del financiador
Simons Foundation	429370

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2020.102030

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abstract = "Let X1,X2,…,Xn be independent random variables, each uniformly distributed on the interval (0,1). We compute the expectation of (X1X2⋯Xn)k⋅∏1≤i(Xj−Xi)2. The result relies on operators, the extended Vandermonde determinant and the hook formula for standard Young tableaux.",

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KW - Uniform random variables

KW - Vandermonde product

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The expectation of the Vandermonde product squared for uniform random variables

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Financiación

ASJC Scopus subject areas

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