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arXiv · 1302.7024

Level set percolation for random interlacements and the Gaussian free field

Pierre-François Rodriguez
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Abstract

We consider continuous-time random interlacements on Z^d, d greater or equal to 3, and investigate the percolation model where a site x of Z^d is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u > 0 exceeds some given non-negative parameter, and empty otherwise. Thus, the set of occupied sites forms a subset of the interlacement at level u. We also investigate percolation properties of empty sites. A recent isomorphism theorem arXiv:1111.4818 of Sznitman enables us to "translate" some of the relevant questions into the language of level-set percolation for the Gaussian free field on Z^d, d greater or equal to 3, for which useful tools have been developed in arXiv:1202.5172. We also gain new insights of independent interest concerning "two-sided" level-set percolation, where a site x of Z^d is occupied if and only if the absolute value of the field variable at that site exceeds a given non-negative level.

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Pierre-François Rodriguez. 2013-02-27. Level set percolation for random interlacements and the Gaussian free field. https://arxiv.org/abs/1302.7024

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