Details

Autor(en) / Beteiligte

• Rodriguez, Pierre-François

Titel

A 0–1 law for the massive Gaussian free field

Ist Teil von

• Probability theory and related fields, 2017-12, Vol.169 (3-4), p.901-930

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2017

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height h . The dependence present in the model is a notorious impediment when trying to analyze the behavior near criticality. Alongside the critical threshold h ∗ for percolation, a second parameter h ∗ ∗ ≥ h ∗ characterizes a strongly subcritical regime. We prove that the relevant crossing probabilities converge to 1 polynomially fast below h ∗ ∗ , which (firmly) suggests that the phase transition is sharp. A key tool is the derivation of a suitable differential inequality for the free field that enables the use of a (conditional) influence theorem.