Sharp inequalities for the mean distance of random points in convex bodies

Gilles Bonnet*, Anna Gusakova, Christoph Thäle, Dmitry Zaporozhets

*Corresponding author voor dit werk

Onderzoeksoutput: ArticleAcademicpeer review

1 Citaat (Scopus)

Samenvatting

For a convex body K⊂Rd the mean distance Δ(K)=E|X1−X2| is the expected Euclidean distance of two independent and uniformly distributed random points X1,X2∈K. Optimal lower and upper bounds for ratio between Δ(K) and the first intrinsic volume V1(K) of K (normalized mean width) are derived and degenerate extremal cases are discussed. The argument relies on Riesz's rearrangement inequality and the solution of an optimization problem for powers of concave functions. The relation with results known from the existing literature is reviewed in detail.

Originele taal-2English
Artikelnummer107813
Aantal pagina's27
TijdschriftAdvances in Mathematics
Volume386
Vroegere onlinedatum4-jun.-2021
DOI's
StatusPublished - 6-aug.-2021
Extern gepubliceerdJa

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