The scaling limit of high-dimensional percolation

ESB 4127

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 asymptotics of k-point connection probabilities, verifying a conjecture of Aizenman and Newman (1984). The proof relies on the lace expansion but is significantly simpler than previous approaches to scaling limits using the lace expansion.