Partial and random covering times in one dimension

We study the recently introduced random walk problems of partial covering time (PCT) and random covering time (RCT). We generalize the concept of first-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...

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Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 63; no. 6 Pt 2; p. 066125
Main Authors Nascimento, M S, Coutinho-Filho, M D, Yokoi, C S
Format Journal Article
LanguageEnglish
Published United States 01.06.2001
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Summary:We study the recently introduced random walk problems of partial covering time (PCT) and random covering time (RCT). We generalize the concept of first-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-dimensional 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 and RCT problems exactly in one dimension.
ISSN:1539-3755
DOI:10.1103/PhysRevE.63.066125