Number of distinct sites visited by a random walker in the presence of a trap

I. Dayan, S. Havlin

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Abstract

The authors study the number of distinct sites visited by a random walker in d=1 after t steps, S(t), in the presence of a trap. They calculate the distribution q(S, t) of S(t) in the limit of large t. They find an unusual crossover in the probability density at S approximately=Sx identical to Dt. For S<<Sx, q(S, t) approximately S-2 and for S>>Sx, q(S, t) approximately St-3/2 exp(-S 2/4Dt). Fro this crossover it follows that the mean number of distinct sites visited is (S(t)) approximately In(t).

Original languageEnglish
Article number008
Pages (from-to)L549-L553
JournalJournal of Physics A: Mathematical and General
Volume25
Issue number9
DOIs
StatePublished - 1992

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