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- W1569647506 abstract "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 $h_{**} geq h_{*}$ 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." @default.
- W1569647506 created "2016-06-24" @default.
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- W1569647506 date "2015-05-29" @default.
- W1569647506 modified "2023-09-23" @default.
- W1569647506 title "A 0-1 law for the massive Gaussian free field" @default.
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