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Fractal behavior in trapping and reaction: A random walk study. (English) Zbl 0587.60062

We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimension \(\tilde d.\) We interpolate between these two limits by introducing a scaling law.
An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimension \(\bar d.\)

MSC:

60G50 Sums of independent random variables; random walks
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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