A
random walk is a
mathematical formalization of a path that consists of a succession of
random steps. For example, the path traced by a
molecule as it travels in a liquid or a gas, the search path of a
foraging animal, the price of a fluctuating
stock and the financial status of a
gambler can all be
modeled as random walks, although they may not be truly random in reality. The term
random walk was first introduced by
Karl Pearson in 1905. Random walks have been used in many fields:
ecology,
economics,
psychology,
computer science,
physics,
chemistry, and
biology. Random walks explain the observed behaviors of many processes in these fields, and thus serve as a fundamental
model for the recorded
stochastic activity.