On the conformally invariant growing mechanism in CLE4

Hao Wu (MIT)

Abstract :

CLE4 is the collection of level lines of GFF. Miller and Sheffield give the first coupling between GFF and CLE4 in the way that loops in the CLE4 are the outmost $\pm\lambda$-height level loop of the field.

From the study of CLE4, we construct a time parameter for each loop in CLE4 such that the time parameter transforms in a conformally invariant way. From this construction of time parameter, we derive the second coupling between GFF and CLE4.

In this talk, we will first give the background of SLE, CLE and GFF. And then, discuss the coupling between GFF and SLE4, the first and the second coupling between GFF and CLE4.