Equality of critical parameters for percolation of Gaussian free field level-sets

Goswami Subhajit
Goswami Subhajit
Rodriguez Pierre-François
Rodriguez Pierre-François
Severo Franco
Severo Franco
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Abstract:

We consider level-sets of the Gaussian free field on $\mathbb Z^d$, for $d\geq 3$, above a given real-valued height parameter $h$. As $h$ varies, this defines a canonical percolation model with strong, algebraically decaying correlations. We prove that three natural critical parameters associated to this model, namely $h_{**}(d)$, $h_{*...More

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