Analysis Seminar

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

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.
Date: Monday, November 16, 2015
Time: 4:10pm
Where: Lunt 105
Contact Person: Antonio Auffinger
Contact email: auffing@math.northwestern.edu
Contact Phone: 847-491-5580
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