random walk

DEFINITION: A “random walk” is a mathematical function on an abstract space, which describes a path through the space consisting of a sequence of steps such that each subsequent step is randomly  related to the prior step.

ETYMOLOGY: For the etymology of the word “random,” see the Glossary article “randomness.”

The noun “walk” derives, via Middle English, from the Old English verb wealcan, meaning “to roll,” “to toss,” or “to journey about.”

The term “random walk” was coined by the mathematician Karl Pearson in 1905.

USAGE: Random walks on one-dimensional spaces, known as a “Markov chains,” play various roles in theoretical physics.

Random walks on two-dimensional spaces play a role in physics and chemistry, for instance, in the representation of Brownian motion.

Random walks on three-dimensional spaces may play a role in biology, as well, notably in the study of protein folding, of animal locomotion, and other phenomena.

In economics, random walks have a variety of uses. Probably the best known of these is economic “random walk theory.”

Economic random walk theory is a mathematical model of the performance of certain markets, notably, the stock exchange, which hypothesizes that changes in stock prices are causally independent of each other, and so related via a random walk.

Economic random walk theory provides a mathematical justification for the commonsense belief that future stock price changes cannot be inferred from past changes.

In other words, the notion of a random walk supports what everybody already knows: namely, that yesterday’s increase in a stock’s price is no guarantee that the price will increase tomorrow.