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

Erwan HillionOliver JohnsonYaming Yu — 2014

ESAIM: Probability and Statistics

We consider probability measures supported on a finite discrete interval [0, ]. We introduce a new finite difference operator ∇, defined as a linear combination of left and right finite differences. We show that this operator ∇ 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...

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