On thin local sets of the Gaussian free field
arXiv:1702.03164
Abstract
We study how small a local set of the continuum Gaussian free field (GFF) in dimension has to be to ensure that this set is thin, which loosely speaking means that it captures no GFF mass on itself, in other words, that the field restricted to it is zero. We provide a criterion on the size of the local set for this to happen, and on the other hand, we show that this criterion is sharp by constructing small local sets that are not thin.
18 pages, 1 beautiful figure. Improved proof of condition for thinness