Non-Markovian reaction sites and trapping

George H. Weiss, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Most models of absorption sites for random walks or diffusion processes fall into one of two categories: (1) Perfect absorption, in which every encounter of a random walker with a trap produces a trapping event, and (2) imperfect absorption in which an encounter leads to a trapping event with probability a < 1. We introduce the notion of a non-Markovian trap characterized by a set of probabilities {fj}, where fj is the probability that they jth encounter leads to a trapping event. Some consequences of this assumption are examined in the context of a one-dimensional trapping problem. It is shown that when the fj have an associated finite first moment the asymptotic survivial probability goes like n 1/2 exp(-an1/3) where n is the step number and a is a constant. This is equivalent to the results one would obtain with a Markovian model. However, when fj is asymptotically proportional to 1/j 1 + α where 0 < α < 1 the survival probability falls off as 1/nα.

Original languageEnglish
Pages (from-to)5670-5672
Number of pages3
JournalJournal of Chemical Physics
Issue number11
StatePublished - 1985


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