  We prove the existence of a class of large global scattering solutions of
Boltzmann's equation with constant collision kernel in two dimensions. These
solutions are found for $L^2$ perturbations of an underlying initial data which
is Gaussian jointly in space and velocity. Additionally, the perturbation is
required to satisfy natural physical constraints for the total mass and second
moments, corresponding to conserved or controlled quantities. The space $L^2$
is a scaling critical space for the equation under consideration. If the
initial data is Schwartz then the solution is unique and again Schwartz on any
bounded time interval.
