Level Lines of Gaussian Free Field II: Whole-Plane GFF
arXiv:1504.04606
Abstract
We study the level lines of GFF starting from interior points. We show that the level line of GFF starting from an interior point turns out to be a sequence of level loops. The sequence of level loops satisfies "target-independent" property. All sequences of level loops starting from interior points give a tree-structure of the plane. We also introduce the continuum exploration process of GFF starting from interior. The continuum exploration process of whole-plane GFF satisfies "reversibility".
41 pages, 14 figures. We updated several references in this version. arXiv admin note: text overlap with arXiv:1302.4738 by other authors