- 05-212 Noam Berger and Marek Biskup
- Quenched invariance principle for simple random walk on percolation clusters
Jun 14, 05
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Abstract. We consider the simple random walk on the (unique) infinite cluster of super-critical percolation in the Euclidean lattice of dimension 2 and higher. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate Brownian motion.