Random walk

In mathematics and physics, a random walk is a formalization of the intuitive idea of taking successive steps, each in a random direction.

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A random walk is a simple stochastic process.

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A random walk is sometimes called a "drunkard's walk".

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Drunkard's Walk is also the name of a 1960 science fiction novel by Frederik Pohl.

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The simplest random walk is a path constructed according to the following rules:

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• There is a starting point.
• The distance from one point in the path to the next is a constant.
• The direction from one point in the path to the next is chosen at random, and no direction is more probable than another.

The average straight-line distance between start and finish points of a random walk of n steps is on the order of sqrt{n}, or more precisely, it asymptotes to sqrt{2 n over pi} pprox 0.8 sqrt{n}. If "average" is understood in the sense of root-mean-square, then the average distance after n steps is higher, but still less than sqrt{n} times the step length.

Random walk: Properties ►



 

Physics: Physics (from the Greek, φυσικός (phusikos), "natural", and φύσις (phusis), "nature") is the science of the natural world in the broadest sense, dealing with matter and energy and the fundamental forces of nature that govern the interaction...

Random: REDIRECT Randomness...

Drunkard's Walk: Drunkard's Walk is a 1960 science fiction novel by Frederik Pohl....




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