There are many different types of random walks, characterized by different specifications with respect to dimensions, the role of time, and whether probabilities remain constant, or are state-dependent.  The theory of random walks is widely used in many fields.  In economics, for example, it might represent price movements of a stock (a one-dimensional model).  In ecology, it might represent the movements of an animal seeking food (a two-dimensional model).  In physics, it might represent the motion of a particle in space (a three-dimensional model).  Often, analysis of the data will attempt to assess whether the behavior differs sufficiently from a random walk to conclude that an alternative model is appropriate.