Volume 18, 2014
|Page(s)||703 - 712|
|Published online||22 October 2014|
A natural derivative on [0, n] and a binomial Poincaré inequality
University of Luxembourg, Campus Kirchberg 1359, Luxembourg
2 Statistics Group, Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK
3 Department of Statistics, University of California, Irvine, CA 92697, USA
Revised: 5 January 2014
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.
Mathematics Subject Classification: 46N30 / 60E15
Key words: Discrete measures / transportation / Poincaré inequalities / Krawtchouk polynomials
© EDP Sciences, SMAI 2014
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.