  We present new scalar and matrix Chernoff-style concentration bounds for a
broad class of probability distributions over the binary hypercube $\{0,1\}^n$.
Motivated by recent tools developed for the study of mixing times of Markov
chains on discrete distributions, we say that a distribution is
$\ell_\infty$-independent when the infinity norm of its influence matrix
$\mathcal{I}$ is bounded by a constant. We show that any distribution which is
$\ell_\infty$-independent satisfies a matrix Chernoff bound that matches the
matrix Chernoff bound for independent random variables due to Tropp. Our matrix
Chernoff bound is a broad generalization and strengthening of the matrix
Chernoff bound of Kyng and Song (FOCS'18). Using our bound, we can conclude as
a corollary that a union of $O(\log|V|)$ random spanning trees gives a spectral
graph sparsifier of a graph with $|V|$ vertices with high probability, matching
results for independent edge sampling, and matching lower bounds from Kyng and
Song.
