Title: Plaquette Percolation in the Torus
Speaker: Paul Duncan - OSU
Abstract: Percolation theory studies sudden changes in the behavior of graphs as vertices or edges are removed at random. Of particular interest is the threshold for the appearance of an infinite connected component in the d-dimensional integer lattice. In 1983 Aizenman et al. introduced plaquette percolation as a higher dimensional analogue. Since then, some progress has been made in the study of codimension 1 plaquettes using their dual relationship to the better understood classical model. However, a satisfactory generalization to all dimensions remains elusive. We consider plaquette percolation with the same local structure in a torus of increasing size. In this model we show that giant cycles appear in middle dimensional plaquettes at p=1/2 and in 1-dimensional plaquettes (edges) at the lattice threshold, along with weaker results in the general case. This is joint work with Matt Kahle and Ben Schweinhart.