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We obtain asymptotic estimates of the Green functions of random walks on the two-dimensional integer lattice that are killed on the horizontal axis. A basic asymptotic formula whose leading term is virtually the same as the explicit formula for the corresponding Green function of Brow- nian motion is established under the existence of second moments only. Some refinement of it is given under a slightly stronger moment condition. The extension of the results to random walks on the higher dimensional lattice is also given.

The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues