论文标题
马尔可夫过程的运输信息不平等的表征
A characterization of transportation-information inequalities for Markov processes in terms of dimension-free concentration
论文作者
论文摘要
已知运输成本和Fisher信息之间的不平等是在其不变措施围绕其不变措施的某些浓度特性的特征。本说明提供了二次传输信息不等式的新特征，$ W_2I $就i.i.d的无维度属性而言。 （在初始位置有条件）基础马尔可夫过程的副本。这与Gozlan的相似之处是二次运输 - 内部不平等$ W_2H $。该证明是基于Feynman-Kac Semogroups的操作员规范的新拉普拉斯型原则，该规范具有独立利益。最后，我们说明了我们的定理和（一种形式）Gozlan的方式是一般凸的分析原理的实例。
Inequalities between transportation costs and Fisher information are known to characterize certain concentration properties of Markov processes around their invariant measures. This note provides a new characterization of the quadratic transportation-information inequality $W_2I$ in terms of a dimension-free concentration property for i.i.d. (conditionally on the initial positions) copies of the underlying Markov process. This parallels Gozlan's characterization of the quadratic transportation-entropy inequality $W_2H$. The proof is based on a new Laplace-type principle for the operator norms of Feynman-Kac semigroups, which is of independent interest. Lastly, we illustrate how both our theorem and (a form of) Gozlan's are instances of a general convex-analytic tensorization principle.
