Jesse Goodman

In invasion percolation, the edges of a graph are assigned i.i.d. edge weights, and an infinite cluster is grown by recursively adding the boundary edge of minimal weight. By considering the edges whose weight is larger than all subsequently accepted...

Run a Brownian motion on a torus for a long time. How large are the random gaps left behind when the path is removed? In three (or more) dimensions, we find that there is a deterministic spatial scale common to all the large gaps anywhere in the...

In two dimensions, many self-interacting processes are described by the Schramm-Loewner Evolution SLE(kappa), a family of random fractal path joining two boundary points of an underlying domain D. These continuous paths arise as the scaling limits of...