We will discuss an exploration process, introduced by Wendelin Werner and Hao Wu, in which conformal loop ensemble (CLE(kappa)) loops grow uniformly from the boundary of a domain. We relate this process in the case kappa = 4 to the set of level loops of the zero-boundary Gaussian free field, and we use this point of view to show that the exploration process is a deterministic function of the CLE loops. We describe how this gives rise to a conformally invariant metric on CLE(4), which we conjecture can be given a natural geometric interpretation.

Based on joint work with Scott Sheffield and Hao Wu.