  Let $G_\Gamma\curvearrowright X$ and $G_\Lambda\curvearrowright Y$ be two
free measure-preserving actions of one-ended right-angled Artin groups with
trivial center on standard probability spaces. Assume they are irreducible,
i.e. every element from a standard generating set acts ergodically. We prove
that if the two actions are stably orbit equivalent (or merely stably
$W^*$-equivalent), then they are automatically conjugate through a group
isomorphism between $G_\Gamma$ and $G_\Lambda$. Through work of Monod and
Shalom, we derive a superrigidity statement: if the action
$G_\Gamma\curvearrowright X$ is stably orbit equivalent (or merely stably
$W^*$-equivalent) to a free, measure-preserving, mildly mixing action of a
countable group, then the two actions are virtually conjugate. We also use
works of Popa and Ioana-Popa-Vaes to establish the $W^*$-superrigidity of
Bernoulli actions of all ICC groups having a finite generating set made of
infinite-order elements where two consecutive elements commute, and one has a
nonamenable centralizer: these include one-ended non-abelian right-angled Artin
groups, but also many other Artin groups and most mapping class groups of
finite-type surfaces.
