Applied Mathematics

Probability Theory

What is a random walk?

Although one might think of a random walk as one that a person takes on the spur of the moment in a part of town he has never walked before, it actually means something totally different in probability theory. A random walk is a random process made up of a discrete sequence of steps, all of a fixed length. For example, in physics, the collisions of molecules in a gas are considered a random walk responsible for diffusion; also in physics, random walks and some of the self-interacting walks are found in quantum field theory. In economics, the “random walk hypothesis” is used to understand and model stock share prices, along with other factors. Biologists use random walks to understand individual animal movements; and geneticists who study population use a random walk to describe the statistical properties of genetic drift. One of the more understandable random walks is familiar to most of us—it is used to estimate the size of the World Wide Web.



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