%0 Generic %1 duminilcopin2020equality %A Duminil-Copin, Hugo %A Goswami, Subhajit %A Rodriguez, Pierre-François %A Severo, Franco %D 2020 %K Percolation %T Equality of critical parameters for percolation of Gaussian free field level-sets %U http://arxiv.org/abs/2002.07735 %X We consider level-sets of the Gaussian free field on $Z^d$, for $d3$, 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 $h_**(d)$, $h_*(d)$ and $h(d)$, respectively describing a well-ordered subcritical phase, the emergence of an infinite cluster, and the onset of a local uniqueness regime in the supercritical phase, actually coincide, i.e. $h_**(d)=h_*(d)= h(d)$ for any $d 3$. At the core of our proof lies a new interpolation scheme aimed at integrating out the long-range dependence of the Gaussian free field. The successful implementation of this strategy relies extensively on certain novel renormalization techniques, in particular to control so-called large-field effects. This approach opens the way to a complete understanding of the off-critical phases of strongly correlated percolation models.

@misc{duminilcopin2020equality, 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 $h_{**}(d)$, $h_{*}(d)$ and $\bar h(d)$, respectively describing a well-ordered subcritical phase, the emergence of an infinite cluster, and the onset of a local uniqueness regime in the supercritical phase, actually coincide, i.e. $h_{**}(d)=h_{*}(d)= \bar h(d)$ for any $d \geq 3$. At the core of our proof lies a new interpolation scheme aimed at integrating out the long-range dependence of the Gaussian free field. The successful implementation of this strategy relies extensively on certain novel renormalization techniques, in particular to control so-called large-field effects. This approach opens the way to a complete understanding of the off-critical phases of strongly correlated percolation models.}, added-at = {2020-02-19T12:00:19.000+0100}, author = {Duminil-Copin, Hugo and Goswami, Subhajit and Rodriguez, Pierre-François and Severo, Franco}, biburl = {https://www.bibsonomy.org/bibtex/216e9815ccd2b02045e5f88887ee3ad03/gzhou}, description = {Equality of critical parameters for percolation of Gaussian free field level-sets}, interhash = {0e070df21690b68464afbfd3b87bcf66}, intrahash = {16e9815ccd2b02045e5f88887ee3ad03}, keywords = {Percolation}, note = {cite arxiv:2002.07735Comment: 54 pages, 5 figures}, timestamp = {2020-02-19T12:00:19.000+0100}, title = {Equality of critical parameters for percolation of Gaussian free field level-sets}, url = {http://arxiv.org/abs/2002.07735}, year = 2020 }