Truncated Connectivities in a Highly Supercritical Anisotropic Percolation Model

摘要

We consider an anisotropic bond percolation model on ?~2, with p=(p_h, p_v)∈[0,1]~2, p_v>p_h, and declare each horizontal (respectively vertical) edge of ?~2 to be open with probability p_h (respectively p_v), and otherwise closed, independently of all other edges. Let x=(x_1, x_2) ∈ ?~2 with 0 ?_p({0 ? x′}). In this note we give an affirmative answer in the highly supercritical regime.