Drunkard’s walk

The simplest and most basic model for the diffusion of atoms across the bulk of a solid is to assume that they move by a series of random jumps, due to the fact that all the atoms are being continually jostled by thermal energy. The path followed is called a random (or drunkard s) walk. It is, at first sight, surprising that any diffusion will take place under these circumstances because, intuitively, the distance that an atom will move via random jumps in one direction would be balanced by jumps in the opposite direction, so that the overall displacement would be expected to average out to zero. Nevertheless, this is not so, and a diffusion coefficient for this model can be defined (see Supplementary Material Section S5). 

One of the simplest models for diffusion is that of the random movement of atoms. The model is generally called a random (or drunkard s) walk.4 A random walk produces a path that is governed completely by random jumps (Fig. S5.3). That is, each individual jump is unrelated to the step before and is governed solely by the probabilities of taking the alternative steps. The application of random walks to diffusion was first made by... 

The site n = 0 is a pure, artificial boundary. The equations can be interpreted as a random walk on — oo < n < oo in which the transitions from — 1 to 0 are impossible a drunkard s walk with a bottomless pit on one side. The total probability is not conserved,... 

Debye was also a much appreciated lecturer at Cornell University in the 50 s—particularly when he illustrated the random nature of diffusion movements by doing his drunkard s walk in front of the class. However, his eagerness to be an effective administrator was not so clearly manifest and after a year as Head of the Chemistry Department, he returned back to full-time research and teaching. 

The problem tackled here is a celebrated one and applies to many phenomena it comes under different names random flight, random walk, drunkard s walk, etc. Suppose a drunken man in the centre of a large field takes n steps each of length /, and suppose that there is no correlation whatsoever between the direction of successive steps how far does he travel on average from the point at which he started It follows from eqn 2.10 that the mean square distance moved is... 

A chain of numbers generated one at a time through a random process is known as a drunkard s walk. The name comes from the chain s appearance when plotted on a graph. 

Mlodinow, Leonard. The Drunkard s Walk How Randomness Rules Our Lives. New York Pantheon, 2008. An explanation of the effects of randomness as a statistical concept and the ways in which it is often misunderstood in the media. 

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