  We investigate the classical Brownian motion of a particle in a
two-dimensional noncommutative (NC) space. Using the standard NC algebra
embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity
induces a non-vanishing correlation between both coordinates at different
times. The effect stands out as a signature of spatial noncommutativity and
thus could offer a way to experimentally detect the phenomena. We further
discuss some limiting scenarios and the trade-off between the scale imposed by
the NC structure and the parameters of the Brownian motion itself.
