Abstract
For a random walk on the integers define R n as the number of (distinct) states visited in the first n steps and Z n as the number of states visited in the first n steps which are never revisited. Here we deal with transient walks. The increments of Z n form a stationary process and various central limit results and an iterated logarithm result are obtained for Z n from known results on stationary processes. Furthermore, the limit behaviour of R n is closely related to that of Z n ; this relationship is elucidated and corresponding limit results for R n are then read off from those for Z n .
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