Average versus typical mean first-passage time in a random random walk.
Average versus typical mean first-passage time in a random random walk.
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随机随机游走中的平均首次通过时间与典型的平均首次通过时间。
DOI：
10.1103/physrevlett.61.500
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发表时间：
1988
影响因子：
8.6
通讯作者：
Goldhirsch
中科院分区：
文献类型：
--
作者：
Noskowicz;Goldhirsch
分析了长度为N的一维随机介质中的随机游动。它严格表明，在大多数实现的介质，平均首次通过时间，t，承担以下关系N，为大N：log t <$N。在介质的实现上的t的平均值< t>满足log < t>N。我们的形式主义，虽然是精确的，只采用了基本的手段，并使随机步行者所经历的延迟的物理学变得透明：这是由于存在子段，在这些子段中，对朝向期望端的运动的偏置是最大的。这些结果有关的副本方法的一些影响进行了简要讨论。
Random walk in a one-dimensional random medium of length N is analyzed. It is rigorously shown that in most realizations of the medium, the mean first-passage time, t, bears the following relation to N, for large N: log t∝ N. The average of t over the realizations of the medium,< t>, satisfies log< t>∝ N. Our formalism, though being exact, employs only elementary means and makes transparent the physics of the delay experienced by the random walker: It is due to the existence of subsegments in which the bias against motion towards the desired end is largest. Some implications of these results concerning the replica method are briefly discussed.