  We consider a white noise perturbation of dynamics in the neighborhood of a
heteroclinic network. We show that under the logarithmic time rescaling the
diffusion converges in distributon in a special topology to a piecewise
constant process that jumps between saddle points along the heteroclinic orbits
of the network. We also obtain precise asymptotics for the exit measure for a
domain containing the starting point of the diffusion.
