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The term random walk is used for a kind of motion (or mathematically-equivalent process) where after some length in one direction, the direction shifts to random direction totally unrelated to the previous direction. The concept is used to describe/model some processes, including some in financial investing, some in biology, as well some in physics, e.g., statistical physics.
For example, in radiative transfer, when a photon is absorbed by an atom, and later one is emitted, the direction of the new photon is random, having no relation to the direction of the one earlier received.
Mathematical (statistical) properties of random walks are studied, one being that the average straight-line distance traveled after N such random travel legs approaches the length of "the square root N" legs, as N is increased. Given the radiative transfer example, this means photons leaving stars have been absorbed and re-emitted on the order of the square of the number of legs (average distance a photon travels before being re-absorbed) that would be necessary if the photon's direction was always outward. For the Sun, a typical leg in the photon's journey is on the order of a centimeter and it can take thousands or perhaps even a million years for a photon to leave the Sun after the creation of the photon (by the heat from fusion in the stellar core) that began the random walk.