相关随机变量的凸距离不等式及其在随机旅行推销员等问题中的应用
The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems
摘要：
证明了满足Dobrushin条件的弱相依随机变量的一般函数的集中不等式。特别是，我们显示Talagrand的凸距离不等式这种类型的依赖。我们将我们的边界的版本的随机推销员的问题，斯坦纳树问题，总磁化的居里-外斯模型与外场，指数随机图模型。我们的证明使用了Chatterjee（2005）引入的证明浓度不等式的可交换对方法。证明的另一个关键成分是$(a,b)$的一个子类-自约束函数，由Boucheron，Lugosi和Massart（2009）引入。
英文摘要：
We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for this type of dependence. We apply our bounds to a version of the stochastic salesman problem, the Steiner tree problem, the total magnetisation of the Curie-Weiss model with external field, and exponential random graph models. Our proof uses the exchangeable pair method for proving concentration inequalities introduced by Chatterjee (2005). Another key ingredient of the proof is a subclass of $(a,b)$-self-bounding functions, introduced by Boucheron, Lugosi and Massart (2009).
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