Abstract
In the present article we consider a general enough set-up and obtain a refinement of the coupling between the Gaussian free field and random interlacements recently constructed by Titus Lupu in [9]. We apply our results to level-set percolation of the Gaussian free field on a $(d+1)$-regular tree, when $d \ge 2$, and derive bounds on the critical value $h_*$. In particular, we show that $0 < h_* < \sqrt{2u_*} $, where $u_*$ denotes the critical level for the percolation of the vacant set of random interlacements on a $(d+1)$-regular tree.
Citation
Alain-Sol Sznitman. "Coupling and an application to level-set percolation of the Gaussian free field." Electron. J. Probab. 21 1 - 26, 2016. https://doi.org/10.1214/16-EJP4563
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