The hitting distribution of a line segment for two dimensional random walks

Abstract

Asymptotic estimates of the hitting distribution of a long segment on the real axis for two dimensional random walks on ${\mathbf{Z}}^2$ of zero mean and finite variances are obtained: some are general and exhibit its apparent similarity to the corresponding Brownian density, while others are so detailed as to involve certain characteristics of the random walk.

arXiv comment22 pages. to appear in Journal of Theoretical Probability