Random Walk

A random walk is a mathematical object describing a path formed by a sequence of random steps, in its simplest form a sequence of positions on the integers that moves one step left or right with equal probability at each turn. The term itself was coined by the statistician Karl Pearson in a 1905 letter to the journal Nature, in which he asked for the probability that a person taking a fixed number of steps of random direction would end up within a given distance of the starting point, though closely related problems, such as the gambler's ruin, had already been studied for centuries. As the number of steps grows large, a simple random walk's rescaled path converges to Brownian motion, making the random walk the natural discrete counterpart of that continuous process, and random walks are used throughout physics, biology, computer science and finance to model diffusion, foraging behavior, search algorithms and the fluctuation of prices.