Definitions for random walk
Random House Webster's College Dictionary
the path of a point or quantity that moves or changes in a stepwise manner, where the direction of each step is statistically random.
Origin of random walk:
a stochastic process consisting of a sequence of changes each of whose characteristics (as magnitude or direction) is determined by chance
A stochastic path consisting of a series of sequential movements, the direction (and sometime length) of which is chosen at random