Trapping of Random Walks in Two and Three Dimensions

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Abstract
We introduce an exact enumeration method for calculating the survival probability P(n) for the n-step random walker on a lattice with randomly distributed high-concentration traps, c. Using it we show that our data scale as lnP(n)≃aρ, where ρ=[−ln(1−c)]2(D+2)nD(D+2), when ρ≳10 in D=2 and D=3 dimensions. This value of ρ corresponds to P(n)≲10−13.