Loop erased random walk, uniform spanning tree, and bi-Laplacian Gaussian field in the critical dimension

Wednesday, September 21, 2016 -
3:00pm to 4:00pm
Critical lattice models are believed to converge to a free field in the scaling limit, at or above their critical dimension. This has been (partially) established for Ising and Phi^4 models for d \ge 4. We describe a simple spin model from uniform spanning forests in Z^d whose critical dimension is 4 and prove that the scaling limit is the bi-Laplacian Gaussian field for d\ge 4. At dimension 4, there is a logarithmic correction for the spin-spin correlation and the bi-Laplacian Gaussian field is a log correlated field. The proof also improves the known mean field picture of LERW in d=4: we show that the renormalized escape probability (and arm events) of 4D LERW converge to some "continuum escaping probability". Based on joint works with Greg Lawler and Xin Sun.
Wei Wu
Courant Institute/NYU
Event Location: 
Fine Hall 214