2013/02/28 by Pierre-François Rodriguez
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP #msc:60G15 #msc:60G55 #msc:60G60 #msc:60K35 #msc:82B43
published as Stoch. Proc. Appl. 124(4), 1469-1502 (2014) · 32 pages, 1 figure
arxiv created 2014/03/26 · arxiv updated 2014/03/28
We consider continuous-time random interlacements on Zd, d greater or equal to 3, and investigate the percolation model where a site x of Zd 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 Zd, 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 Zd is occupied if and only if the absolute value of the field variable at that site exceeds a given non-negative level.