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### 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 language | English |
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Pages (from-to) | 703-712 |

Journal | ESAIM. Probability and Statistics |

Volume | 18 |

Early online date | 17 Apr 2014 |

DOIs | |

Publication status | Published - 22 Oct 2014 |

## Fingerprint Dive into the research topics of 'A natural derivative on [0,n] and a binomial Poincaré inequality'. Together they form a unique fingerprint.

## Projects

- 1 Finished

## Cite this

Hillion, E., Johnson, O. T., & Yu, Y. (2014). A natural derivative on [0,n] and a binomial Poincaré inequality.

*ESAIM. Probability and Statistics*,*18*, 703-712. https://doi.org/10.1051/ps/2014007