A central limit theorem for "critical" furst-passage percolation in two dimensions

Abstract

Consider (independent) first-passage percolation on the edges of ℤ2. Denote the passage time of the edge e in ℤ2 by t(e), and assume that P{t(e) = 0} = 1/2, P{0 < t(e) < C0} = 0 for some constant C0 > 0 and that E[tδ(e)] < ∞ for some δ > 4. Denote by b0,n the passage time from 0 to the halfplane {(x, y): x ≧ n}, and by T(0, nu) the passage time from 0 to the nearest lattice point to nu, for u a unit vector. We prove that there exist constants 0 < C1, C2 < ∞ for some δ > 4.