We study the speed of a biased random walk on a percolation cluster on ℤd in function of the percolation parameter p. We obtain a first order expansion of the speed at p=1 which proves that percolating slows down the random walk at least in the case where the drift is along a component of the lattice.
"The speed of a biased random walk on a percolation cluster at high density." Ann. Probab. 38 (5) 1717 - 1782, September 2010. https://doi.org/10.1214/09-AOP521