A natural derivative on [0,  n] and a binomial Poincaré inequality. (22nd October 2014)

• Record Type: Journal Article
• Authors: Hillion, Erwan; Johnson, Oliver; Yu, Yaming
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 703
• Page End: 712
• Publication Date: 2014-10-22
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2014007
• Languages: English
• ISSNs: 1292-8100

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We consider probability measures supported on a finite discrete interval [0,  <italic>n</italic>]. We introduce a new finite difference operator ∇_{<italic>n</italic>}, defined as a linear combination of left and right finite differences. We show that this operator ∇_{<italic>n</italic>} plays a key role in a new Poincaré (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk polynomials acting as eigenfunctions of the relevant operator. We briefly discuss the relationship of this operator to the problem of optimal transport of probability measures.</p> </abstract>