Nearest-neighbor Walks with Low Predictability Proole and Percolation in 2 + " Dimensions
نویسنده
چکیده
A few years ago, Grimmett, Kesten and Zhang proved that for supercritical bond percolation on Z 3 , simple random walk on the innnite cluster is a.s. transient. We generalize this result to a class of wedges in Z 3 including, for any " 2 (0; 1), the wedge W " = f(x; y; z) 2 Z 3 : x 0; jzj x " g which can be thought of as representing a (2 + ")-dimensional lattice. Our proof builds on recent work of Benjamini, Pemantle and Peres, and involves the construction of nite-energy ows using nearest-neighbor walks on Z with low predictability proole. Along the way, we obtain some new results on attainable decay rates for predictability prooles of nearest-neighbor walks.
منابع مشابه
Nearest-Neighbor Walks With Low Predictability Profile and Percolation in 2+ε Dimensions
A few years ago, Grimmett, Kesten and Zhang proved that for supercritical bond percolation on Z3, simple random walk on the infinite cluster is a.s. transient. We generalize this result to a class of wedges in Z3 including, for any ε ε (0,1), the wedge Wε={(x,y,z) ε Z3 : x ≥ 0, |z| ≤ x ε} which can be thought of as representing a (2 + ε)-dimensional lattice. Our proof builds on recent work of B...
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