Abstract
We consider the probability that a two-dimensional random walk starting at the origin never returns to the half-line (-∞,0]×{0} before time n. It is proved that for aperiodic random walk with mean zero and finite 2+∂(>2)-th absolute moment, this probability times n^<1/4> converges to some positive constant c^* as n→∞. Our investigation of this probability is motivated by the study of the DLA model. In the first half of this paper, we give an explanation of the DLA model and its related works. In the latter half, we outline the proof of our results.
