Quenched invariance principle for simple random walk on clusters in correlated percolation models Academic Article uri icon


  • © 2015, Springer-Verlag Berlin Heidelberg. We prove a quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Zd, d≥ 2 , with long-range correlations introduced in (Drewitz et al. in J Math Phys 55(8):083307, 2014), solving one of the open problems from there. This gives new results for random interlacements in dimension d≥ 3 at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness (which is believed to coincide with the whole supercritical regime). An essential ingredient of our proof is a new isoperimetric inequality for correlated percolation models.

author list (cited authors)

  • Procaccia, E. B., Rosenthal, R., & Sapozhnikov, A.

citation count

  • 14

publication date

  • December 2016