论文标题
高斯log-sobolev不平等和倒数不平等的赤字
The deficit in the Gaussian log-Sobolev inequality and inverse Santalo inequalities
论文作者
论文摘要
我们建立了涉及相对熵，渔民信息和逆向Santal {ó}不等式的最佳运输成本的双等效形式。我们特别表明，Mahler的猜想等于高斯对数Sobolev不平等的不足的一定维下限。我们还从现有的结果中得出了反向Santal {ó}不平等现有的结果，在高斯对数Sobolev不平等的不足方面有些急剧下降。
We establish dual equivalent forms involving relative entropy, Fisher information and optimal transport costs of inverse Santal{ó} inequalities. We show in particular that the Mahler conjecture is equivalent to some dimensional lower bound on the deficit in the Gaussian logarithmic Sobolev inequality. We also derive from existing results on inverse Santal{ó} inequalities some sharp lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality.
