Abstract
The CTRW has often been applied to problems related to transport in a statistically homogeneous disordered medium, which means that there are no traps or reflecting boundaries to be found in the medium. Two physical applications, one to the migration of photons in a turbid medium and the second to the theory of diffusion-controlled reactions in a random medium, suggest that it might be useful to study properties of the CTRW, particularly as they refer to survival probability in the presence of a trap or a trapping surface. We calculate a number of these properties when the pausing-time density is asymptotically proportional to a stable law, i.e.,ψ(t)∼T α+1 as (t/T)→∞, where 0<α<1. A forthcoming paper will establish the correspondence between properties of the CTRW and proprties of random walkers on a fractal with trapping boundaries.
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This paper is dedicated to Jerry Percus on the occasion of his 65th birthday. May he enjoy many more happy and productive years.
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Weiss, G.H., Havlin, S. Some properties of a fractal-time continuous-time random walk in the presence of traps. J Stat Phys 63, 1005–1018 (1991). https://doi.org/10.1007/BF01029995
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DOI: https://doi.org/10.1007/BF01029995