EVENT DETAILS AND ABSTRACT

Title: Bi-Laplacian Gaussian field and Uniform Spanning Forests
Speaker: Xin Sun
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

In this talk, I will first review Gaussian free field in $\R^d$ and its generalization called fractional Gaussian field, which includes log correlated field and bi-Laplacian Gaussian field as examples. Fractional Gaussian field arises naturally as scaling limits of spin models, e.g. Ising model and phi^4 model, at or above their critical dimension for the mean field behavior. 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 Gaussain field for $d\ge 4$. At dimension 4, there is a $log n$ correction for the spin-spin correlation and the bi-Laplacian Gaussian field is a log correlated field. Based on a joint work with Greg Lawler and Wei Wu and a survey with Asad Lodhia, Scott Sheffield and Sam Watson.