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原文連結
論文資訊
- 類型：已發表論文
- 日期：2018
摘要
We determine how long a diffusing particle spends in a given spatial range before it dies at an absorbing boundary. In one dimension, for a particle that starts at x(0) and is absorbed at x = 0, the average residence time of the particle in the range [x, x + dx] is T(x) = x/D dx for x < x(0) and x(0)/D dx for x > x(0), where D is the 擴散 coeffcient. We extend our approach to biased 擴散, to a particle confined to a finite interval, and to general spatial dimensions. We then use the generating function technique to derive parallel results for the average number of times that a one-dimensional symmetric nearest-neighbor random walk visits site x when the walk starts at x(0) = 1 and is absorbed at x = 0. We also determine the distribution of times when the random walk first revisits x = 1 before
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