Level Lines of Gaussian Free Field II: Whole-Plane GFF
Probability
2016-08-19 v3
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".
Keywords
Cite
@article{arxiv.1504.04606,
title = {Level Lines of Gaussian Free Field II: Whole-Plane GFF},
author = {Menglu Wang and Hao Wu},
journal= {arXiv preprint arXiv:1504.04606},
year = {2016}
}
Comments
41 pages, 14 figures. We updated several references in this version. arXiv admin note: text overlap with arXiv:1302.4738 by other authors