A natural derivative on [0, n ] and a binomial Poincaré inequality
A natural derivative on [0, n ] and a binomial Poincaré inequality
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[0, n ] 上的自然导数和二项式庞加莱不等式
DOI：
10.1051/ps/2014007
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Hillion E
中科院分区：
文献类型：
--
作者：
Hillion E
我们考虑在有限离散区间[0，n]上支持的概率测度。我们引入了一个新的有限差分算子∇n，定义为左右有限差分的线性组合。我们证明了算子∇n在一个新的关于二项式权值的poincar<s:1>（谱隙）不等式中起着关键作用，其中正交Krawtchouk多项式作为相关算子的特征函数。我们简要地讨论了该算子与概率测度的最优转移问题的关系。
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.