We show that random walks on the infinite supercritical percolation clusters in Z^d satisfy the usual Law of the Iterated Logarithm. The proof combines Barlow's Gaussian heat kernel estimates and the ergodicity of the random walk on the environment viewed from the random walker as derived by Berger and Biskup.
Coupling between Brownian motion and random walks on the infinite percolation cluster
Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks
Exponential inequalities and laws of the iterated logarithm for multiple Poisson--Wiener integrals and Poisson $U$-statistics
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