利用马尔可夫收缩求测度集中度
Obtaining Measure Concentration from Markov Contraction
摘要：
非乘积、非Haar测度的浓度界是最近才得到的：Marton在1996年通过耦合方法得到了收缩马尔可夫链的第一个这样的结果。接下来的工作，除了少数例外，也使用了耦合。虽然这种技术作为一种理论工具无疑是有用的，但它并不总是简单的应用。作为一种替代耦合，我们使用的基本马尔可夫收缩引理，以获得简单的，有用的，显然是新颖的浓度结果为各种马尔可夫型过程。我们的技术包括将概率表示为矩阵乘积，并将马尔可夫收缩应用于这些表达式;因此，它是相当普遍的，并有可能在这方面产生进一步的结果。
英文摘要：
Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996 via the coupling method. The work that followed, with few exceptions, also used coupling. Although this technique is of unquestionable utility as a theoretical tool, it is not always simple to apply. As an alternative to coupling, we use the elementary Markov contraction lemma to obtain simple, useful, and apparently novel concentration results for various Markov-type processes. Our technique consists of expressing probabilities as matrix products and applying Markov contraction to these expressions; thus it is fairly general and holds the potential to yield further results in this vein.
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