The speed of a biased random walk on a percolation cluster at high density
arXiv:0812.2532
Abstract
We study the speed of a biased random walk on a percolation cluster on $\Z^d$ 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.
65 pages, 5 figures. Published at Ann. Probab. Volume 38, Number 5 (2010), 1717-1782