Article (Scientific journals)
A natural derivative on [0, n] and a binomial Poincaré inequality
Hillion, Erwan; Johnson, Oliver; Yu, Yaming
2014In ESAIM: Probability and Statistics, 18, p. 703--712
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Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Hillion, Erwan ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Johnson, Oliver
Yu, Yaming
Language :
English
Title :
A natural derivative on [0, n] and a binomial Poincaré inequality
Publication date :
2014
Journal title :
ESAIM: Probability and Statistics
ISSN :
1262-3318
Publisher :
Les Ulis/EDP Sciences, Paris, France
Volume :
18
Pages :
703--712
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 26 February 2015

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