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 Level set percolation for random interlacements and the Gaussian free field


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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 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. 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.



Author: Pierre-Fran├žois Rodriguez

Source: https://archive.org/







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