## Abstract

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 {f_{j}}, where f_{j} 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 f_{j} have an associated finite first moment the asymptotic survivial probability goes like n ^{1/2} exp(-an^{1/3}) 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 f_{j} is asymptotically proportional to 1/j ^{1 + α} where 0 < α < 1 the survival probability falls off as 1/nα.

Original language | English |
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Pages (from-to) | 5670-5672 |

Number of pages | 3 |

Journal | Journal of Chemical Physics |

Volume | 83 |

Issue number | 11 |

DOIs | |

State | Published - 1985 |