Abstract
This chapter discusses the rate of escape problem for a class of random walks. The rate of escape problem was first considered for simple random walk in dimension d ≥ 3 by Dvoretzky and Erdös. The only known result that applies to all symmetric distributions for the summands is by Kesten who proved Erickson's conjecture that in dimension d ≥ 3, any random walk escapes at least as fast as simple random walk.
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