TY - JOUR

T1 - Number of distinct sites visited by a random walker in the presence of a trap

AU - Dayan, I.

AU - Havlin, S.

PY - 1992

Y1 - 1992

N2 - 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<x, 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).

AB - 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<x, 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).

UR - http://www.scopus.com/inward/record.url?scp=0141571790&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/25/9/008

DO - 10.1088/0305-4470/25/9/008

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AN - SCOPUS:0141571790

SN - 0305-4470

VL - 25

SP - L549-L553

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 9

M1 - 008

ER -