In an earlier paper, the author and Fitzsimmons resolved several problems about the intersections of Brownian motions and Levy processes, using projection techniques to construct certain measures of finite energy. The present paper aims to make these techniques more accessible, by treating an analogous but simpler problem. Upper bounds will be obtained on intersection probabilities for discrete time Markov chains. This will be applied to obtain a Wiener type test for intersections of random walks within given sets.



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