ENTROPIC RICCI CURVATURE BOUNDS FOR DISCRETE INTERACTING SYSTEMS
ENTROPIC RICCI CURVATURE BOUNDS FOR DISCRETE INTERACTING SYSTEMS
复制标题
DOI：
10.1214/15-aap1133
复制
发表时间：
2016-06-01
影响因子：
1.8
通讯作者：
Maas, Jan
中科院分区：
文献类型：
--
作者：
Fathi, Max;Maas, Jan
提出了一种新的系统的方法来证明离散集上马尔可夫链的熵Ricci曲率下界。使用不同的方法，最近在几个例子中（例如，一维生灭链、生成链、伯努利-拉普拉斯模型和随机转置模型）得到了这样的界。然而，一直缺乏求得离散里奇界的一般方法。我们的方法涵盖了上面所有的例子。此外，我们还得到了完全图上零范围过程的新的Ricci曲率界。该方法受到Caputo， Dai Pra和Posta最近关于离散泛函不等式的工作的启发。
We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli-Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition, we obtain new Ricci curvature bounds for zero-range processes on the complete graph. The method is inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities.