SCALING LIMITS OF PARTICLE SYSTEMS
It has long been known that scaling limits of critical branching random walks lead to an interesting measure valued process, now called super-Brownian motion. Here we describe recent results which show that in two or more dimensions super-Brownian motion is the limit of rescaled contact processes and voter models. To get more interesting limits in d=2 or 3 one can (we think) take multitype contact processes like the colicin systems of Durrett and Levin (1997) and let the interaction parameters between species get large at the right rate to get convergence to models that generalize the interacting super-Brownian motions constructed by Evans and Perkins (1998). Some theorems and simulations will be shown in support of this picture.