title: Partial and random covering times in one dimension.
abstract: 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.
authors: Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil.
authors: M S
authors: MS
authors: Nascimento
authors: M D
authors: MD
authors: Coutinho-Filho
authors: C S
authors: CS
authors: Yokoi