A natural derivative on [0,n] and a binomial Poincaré inequality

Erwan Hillion, Oliver T Johnson, Yaming Yu

Research output: Contribution to journalArticle (Academic Journal)

4 Citations (Scopus)

Abstract

We consider probability measures supported on a finite discrete interval [0, n]. We introduce a new finite difference operator ∇n, defined as a linear combination of left and right finite differences. We show that this operator ∇n 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.
Original languageEnglish
Pages (from-to)703-712
JournalESAIM. Probability and Statistics
Volume18
Early online date17 Apr 2014
DOIs
Publication statusPublished - 22 Oct 2014

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