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

Erwan Hillion; Oliver Johnson; Yaming Yu

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 703-712
- ISSN: 1292-8100

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topHillion, Erwan, Johnson, Oliver, and Yu, Yaming. "A natural derivative on [0, n] and a binomial Poincaré inequality." ESAIM: Probability and Statistics 18 (2014): 703-712. <http://eudml.org/doc/274381>.

@article{Hillion2014,

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.},

author = {Hillion, Erwan, Johnson, Oliver, Yu, Yaming},

journal = {ESAIM: Probability and Statistics},

keywords = {discrete measures; transportation; poincaré inequalities; Krawtchouk polynomials; Poincaré inequalities},

language = {eng},

pages = {703-712},

publisher = {EDP-Sciences},

title = {A natural derivative on [0, n] and a binomial Poincaré inequality},

url = {http://eudml.org/doc/274381},

volume = {18},

year = {2014},

}

TY - JOUR

AU - Hillion, Erwan

AU - Johnson, Oliver

AU - Yu, Yaming

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

JO - ESAIM: Probability and Statistics

PY - 2014

PB - EDP-Sciences

VL - 18

SP - 703

EP - 712

AB - 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.

LA - eng

KW - discrete measures; transportation; poincaré inequalities; Krawtchouk polynomials; Poincaré inequalities

UR - http://eudml.org/doc/274381

ER -

## References

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