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first passage percolation
First passage percolation is a mathematical method used to describe the paths reachable in a random medium within a given amount of time.
==Introduction==
First passage percolation is a subset of percolation theory, specifically Bernoulli percolation, and was first introduced by John Hammersley and Dominic Welsh in 1965. There are two different methods of calculating any kind of percolation: bond percolation and site percolation. This article will deal mostly with bond percolation, as this is where most of the work on first passage percolation has been done, but there are other articles which talk about site percolation.
Bernoulli percolation is a percolation model in which, starting at a specified initial node, each attached link is either followed or not followed by a specified probability (where is the probability of the following the link and is the probability of not following this link). First passage percolation differs from Bernoulli percolation by assigning a different value, or different Weight, to each link, as opposed to having the same value used for every link in the system. The goal of first passage percolation is look at all the paths that can be reached, each described by the sum of individual weights in the path. Many times the goal is to find the path with the least weight, or Geodesic.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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