We argue that dependent versions of McDiarmid's inequality are a useful but underutilized tool in mathematical statistics, learning theory and theoretical computer science. To make this point, we first highlight that approximate tensorization of entropy (ATE) implies McDiarmid's via the Entropy Method. Second, we derive McDiarmid's inequality for non-isotropic Gaussian random vectors $X \sim \mathcal N(μ, Σ)$ through ATE with a constant of the order of the condition number of $Σ$. We both independently obtain this ATE through a simple application of stochastic localization and also discuss how a more general ATE for the Gibbs sampler due to Ascolani et al., 2026 generalizes McDiarmid's-like concentration to strongly log-concave and log-smooth probability measures. We then apply the resulting concentration inequalities to resolve a question on the concentration of $\operatorname{sign}(X)$ posed by Simone Bombari, investigate Erdős-Rényi graphs under dependence and prove a Dvoretzky-Kiefer-Wolfowitz-type inequality for observations from a joint measure fulfilling ATE and continuous marginal CDFs. For the class of strongly log-concave and log-smooth measures, this result improves upon a prior Dvoretzky-Kiefer-Wolfowitz-type inequality for non-i.i.d. observations due to Bobkov and Götze, 2010, by establishing the expected $1/\sqrt{n}$-rate of convergence under weak dependence instead of $n^{-1/3}$.

翻译：我们论证了依赖情形下的McDiarmid不等式是数理统计、学习理论与理论计算机科学中实用但未被充分利用的工具。为阐明这一点，我们首先指出熵的近似张量化（ATE）可通过熵方法推导出McDiarmid不等式。其次，我们通过ATE以$\Sigma$条件数量级的常数，推导出非各向同性高斯随机向量$X \sim \mathcal N(μ, Σ)$的McDiarmid不等式。我们既通过随机局部化的简单应用独立获得此ATE，也讨论了Ascolani等人（2026）提出的针对吉布斯采样的更一般ATE如何将类似McDiarmid的集中性推广到强对数凹与对数光滑概率测度。随后，我们将所得集中不等式应用于解决Simone Bombari提出的关于$\operatorname{sign}(X)$集中性的问题，研究依赖情形下的Erdős-Rényi图，并证明对于满足ATE及连续边际CDF的联合测度观测值的Dvoretzky-Kiefer-Wolfowitz型不等式。对于强对数凹与对数光滑测度类，该结果通过建立弱依赖下预期的$1/\sqrt{n}$收敛速率（替代$n^{-1/3}$），改进了Bobkov与Götze（2010）提出的非独立同分布观测值的Dvoretzky-Kiefer-Wolfowitz型不等式。