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On thin local sets of the Gaussian free field. (English. French summary) Zbl 1450.60010
Summary: We study how small a local set of the continuum Gaussian free field (GFF) in dimension \(d\) 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.

MSC:
60D05 Geometric probability and stochastic geometry
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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