A Linear Programming Inequality with Applications to Concentration of Measure
نویسنده
چکیده
Over the past decade there has been a flurry of new concentration of measure inequalities; we refer the reader to [4] for an in-depth survey, or [2, 3, 5] for some more recent advances. In [2] the martingale difference method was employed in a novel way to obtain a general concentration inequality for dependent random variables, with respect to the (unweighted) Hamming metric. At the core of that approach lies a certain linear programming inequality associated with bounding martingale differences [2, Theorem 4.8]. In this paper, we give a considerably simpler proof of a rather more general result, extending it to the weighted Hamming metrics. The applications to measure concentration are immediate (culminating in Corollary 3.3); additionally, it is hoped that the linear programming inequality and the technique employed for proving it will find further applications. Since the main focus of this paper is the inequality in Theorem 2.5, we forgo a detailed discussion of measure concentration and how our bound relates to existing results. Such a discussion may be found in [2, 3].
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