Robert Fitzner: Non-backtracking lace expansion

Many spatial interacting models are in high-dimension expected to behave similar to a corresponding simple model without interactions, such as simple random walk and branching random walk. In this talk I introduce the concept of mean-field behavior and discuss a method to prove it. We apply these ideas to key models in statistical physics, namely, self-avoiding walk, percolation, lattice trees and lattice animals.

We focus on a novel method call Non-backtracking lace expansion, which can be used to study nearest-neighbor models in dimensions above, but close to, the upper critical dimension above which mean-field behavior is expected.