Jon Warren

At the edge of a cloud of Brownian particles

The talk concerns a model for the motion of particles carried in a turbulent fluid in which a single particle moves according to an SDE of the form dX_t= \sigma dB_t + dW(t,X_t). Here, W is a Gaussian field, describing the environment, and B is an independent Brownian motion representing some additional diffusivity. We are interested in the behaviour at large times, but far from the origin. There, we find a transition which is analogous to that between weak and strong disorder for polymer models, and at the transition the stochastic heat equation appears.