Mathematics

Various growth processes for conformal maps with branching, such as Diffusion Limited Aggregation (DLA) were suggested by physicists in the 1980s. Despite spectacular numerical simulations, there are few rigorous mathematical results in the area.I will discuss a new form of stochastic Loewner evolution that is designed for the study of such processes. The main new idea is to use Dyson Brownian motion, coupled with natural branching rules, as the driving measure of a Loewner evolution. The main advantage of this method is that yields new stochastic PDE as a scaling limit.