# Random walk

## Process forming a path from many random steps / From Wikipedia, the free encyclopedia

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In mathematics, a **random walk**, sometimes known as a **drunkard's walk**, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.

An elementary example of a random walk is the random walk on the integer number line $\mathbb {Z}$ which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term *random walk* was first introduced by Karl Pearson in 1905.^{[1]}

Realizations of random walks can be obtained by Monte Carlo simulation.^{[2]}