Number of distinct sites visited by a random walker in the presence of a trap
I Dayan; S Havlin; I Dayan; Dept. of Phys., Bar-Ilan Univ., Ramat-Gan, Israel; S Havlin; Dept. of Phys., Bar-Ilan Univ., Ramat-Gan, Israel
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1992-05-07
Аннотация:
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=S<sub>x</sub> identical to Dt. For S<<S<sub>x</sub>, q(S, t) approximately S<sup>-2</sup> and for S>>S<sub>x</sub>, q(S, t) approximately St<sup>-3/2</sup> exp(-S<sup>2/4</sup>Dt). Fro this crossover it follows that the mean number of distinct sites visited is (S(t)) approximately In(t).
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