We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition recovers local differential privacy (LDP) for $c\to 0$. We derive achievable bounds on contraction in terms of a kernels PML guarantees, and provide mechanism constructions that achieve the presented bounds. Further, we extend the results to general $f$-divergences by an application of Binette's inequality. Our analysis yields tighter bounds for mechanisms satisfying LDP and extends beyond the LDP regime to any discrete kernel.

翻译：我们研究了离散马尔可夫核的Dobrushin系数，这些核在所有具有最小概率质量以常数$c>0$有界远离零的分布上具有有界逐点最大泄漏（PML）。当$c\to 0$时，该定义可恢复局部差分隐私（LDP）。我们根据核的PML保证推导了收缩性的可达界，并提供了实现所提出边界的机制构造。此外，通过应用Binette不等式，我们将结果推广到一般的$f$-散度。我们的分析为满足LDP的机制提供了更严格的边界，并将研究范围扩展到LDP机制之外的所有离散核。