Partial and random covering times in one dimension - art. no. 066125

We study the recently introduced random walk problems of partial covering t ime (PCT) and random covering time (RCT). We generalize the concept of firs t-passage time to a given set of m sites by considering the probability of visiting all m sites for the first time on the tth step. For the one-dimens ional case we derive an explicit result for the mean time needed to visit m sites for the first time. Using this result we are able to solve the PCT a nd RCT problems exactly in one dimension.