Let
be a stratum of translation surfaces with at least two singularities, let
denote the Masur-Veech measure on
, and let
be a flow on
obtained by integrating a Rel vector field. We prove that
is mixing of all orders, and in particular is ergodic. We also characterize the ergodicity of flows defined by Rel
... [Show full abstract] vector field, for more general spaces , where is an orbit-closure for the action of (i.e., an affine invariant subvariety) and is the natural measure. Our results are conditional on a forthcoming measure classification result of Brown, Eskin, Filip and Rodriguez-Hertz.