We study the question of whether submodular functions of random variables satisfying various notions of negative dependence satisfy Chernoff-like concentration inequalities. We prove such a concentration inequality for the lower tail when the random variables satisfy negative association or negative regression, partially resolving an open problem raised in (Qiu and Singla [QS22]). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms (Chekuri, Vondrak, and Zenklusen [CVZ10] and Harvey and Olver [HO14]). We discuss some applications of our results to combinatorial optimization and beyond. We also show applications to the concentration of read-k families [Gav+15] under certain forms of negative dependence; we further show a simplified proof of the entropy-method approach of [Gav+15].

翻译：本文研究满足各类负相关性质的随机变量子模函数是否满足Chernoff型集中不等式的问题。当随机变量满足负关联性或负回归性时，我们证明了其下尾的集中不等式，部分解决了(Qiu和Singla [QS22])中提出的公开问题。先前研究仅针对特定依赖舍入算法生成的随机变量证明了此类集中结果(Chekuri, Vondrak和Zenklusen [CVZ10]以及Harvey和Olver [HO14])。我们探讨了该结果在组合优化及其他领域的应用潜力。同时展示了特定负相关形式下read-k族[Gav+15]的集中性应用，并进一步给出了[Gav+15]中熵方法证明的简化形式。