Velocity Differences as a Probe of Non--Gaussian Density Fields

We examine the multi--point velocity field for non--Gaussian models as a probe of non--Gaussian behavior. The two--point velocity correlation is not a useful indicator of a non--Gaussian density field, since it depends only on the power spectrum, even for non--Gaussian models. However, we show that the distribution of velocity differences $\bfv_1 - \bfv_2$, where $\bfv_1$ and $\bfv_2$ are measured at the points $\bfr_1$ and $\bfr_2$, respectively, is a good probe of non--Gaussian behavior, in that $p(\bfv_1 - \bfv_2)$ tends to be non--Gaussian whenever the density field is non--Gaussian. As an example, we examine the behavior of $p(\bfv_1 - \bfv_2)$ for non--Gaussian seed models, in which the density field is the convolution of a distribution of points with a set of density profiles. We apply these results to the global texture model.