We consider full scaling limits of planar nearcritical percolation in the Quad-Crossing-Topology introduced by Schramm … other. The results hold for percolation models on rather general lattices, including bond percolation on the square lattice … and site percolation on the triangular lattice. …

We prove an apparently new type of ergodic theorem, and apply it to the site percolation problem on sparse random …

We consider continuous-time random interlacements on Zd, d≥3, and investigate the percolation model where a site x of … 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 …

the planar invasion percolation cluster. The first part of the paper is devoted to proving an almost sure analogue of H …. Kesten’s subdiffusivity theorem for the random walk on the incipient infinite cluster and the invasion percolation cluster … Kesten’s original argument, leading to an explicit almost sure lower bound for τ(n) in terms of percolation arm exponents …

probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the …

focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one …