Tom Hutchcroft

It is conjectured that many models of statistical mechanics have a rich, fractal-like behaviour at and near their points of phase transition, with power-law scaling governed by critical exponents that are expected to depend on the dimension but not...

Event Organizers Gordon Slade University of British Columbia Omer Angel University of British Columbia Louigi Addario-Berry McGill University Mathav Murugan University of British Columbia Course Descriptions Main course: Tom Hutchcroft Title...

I will give an overview of forthcoming work proving that large critical percolation clusters in high-dimensional lattices converge under rescaling to the expected universal limit object: superBrownian motion. A key step is to compute the first-order...

For deterministic bounded degree triangulations, circle packing has proven a powerful tool for studying random walk via geometric arguments. In this talk, I will discuss extensions and analogues for random triangulations without the assumption of...

In the 1980’s, Aldous and Broder independently proved that the collection of first-entry edges of a random on a finite graph is distributed as a uniform spanning tree of the graph; using this fact to sample the uniform spanning tree of a finite graph...

The uniform spanning forests (USFs) of an infinite graph G are defined to be infinite volume limits of uniformly chosen spanning trees of finite subgraphs of G. These limits can be taken with respect to two extremal boundary conditions, yielding the...

In 1987, Aizenman, Kesten, and Newman proved that percolation on Z^d always has at most one infinite cluster a.s. While their proof has mostly been eclipsed by the more general and arguably more elegant proof of Burton and Keane, the Aizenman-Kesten...