Level set percolation for random interlacements and the Gaussian free field

Pierre-François Rodriguez

Stochastic Processes and their Applications, 2014, vol. 124, issue 4, 1469-1502

Abstract: We consider continuous-time random interlacements on Zd, d≥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 constant α≥0, and empty otherwise. We also examine percolation properties of empty sites. A recent isomorphism theorem (Sznitman, 2012) enables us to “translate” some of the relevant questions into the language of level-set percolation for the Gaussian free field on Zd, d≥3, about which new insights of independent interest are also gained.

Keywords: Percolation; Long-range dependence; Gaussian free field; Random interlacements; Level sets (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2013.12.009

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