UBC Mathematics Department
Brownian motion has played a major role in statistical mechanics
for a long time. Super-Brownian motion is a more recent construct,
which can be used to model tree-based random mass distributions.
This lecture will describe recent work showing that super-Brownian
motion arises naturally as a scaling limit in the critical behaviour
of two statistical mechanical models:
1. lattice trees, a combinatorial model (joint work with Derbez), and
2. percolation, a probabilistic model (joint work with Hara).