  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.
