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, resolving an open problem raised in (\citet{approx/QiuS22}). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms (\citet{focs/ChekuriVZ10,soda/HarveyO14}). We discuss some applications of our results to combinatorial optimization and beyond.

翻译：我们研究满足不同负依赖概念的随机变量的子模函数是否具有类似Chernoff的集中不等式问题。我们证明了当随机变量满足负关联或负回归时下尾部的集中不等式，解决了(\citet{approx/QiuS22})提出的一个开放问题。以往研究仅针对来自特定依赖舍入算法的随机变量证明了此类集中结果(\citet{focs/ChekuriVZ10,soda/HarveyO14})。我们讨论了这些结果在组合优化及其他领域的若干应用。