Probability Seminar: Vivian Healey

In its most well-known form, the Loewner equation gives a correspondence between curves in the upper half-plane and continuous real functions (called the “driving function” for the equation). We consider the generalized Loewner equation, where the driving function has been replaced by a time-dependent real measure. In the first part of the talk, we investigate the delicate relationship between the driving measure and the generated hull. We show that certain discrete driving measures (closely related to branching Dyson Brownian motion) generate tree embeddings. In the second part of the talk, we describe the superprocess that is the scaling limit of branching Dyson Brownian motion when the underlying (critical, binary) Galton-Watson trees are conditioned to converge to the continuum random tree.