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Level set percolation for random interlacements and the Gaussian free field

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  • Rodriguez, Pierre-François

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.

Suggested Citation

  • Rodriguez, Pierre-François, 2014. "Level set percolation for random interlacements and the Gaussian free field," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1469-1502.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:4:p:1469-1502
    DOI: 10.1016/j.spa.2013.12.009
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