A random walk is a stochastic process describing a path formed by a sequence of random steps, each step’s direction and size drawn from a probability distribution independent of the path’s prior history in the simplest (Markovian) case. It underlies graph embedding techniques such as node2vec and DeepWalk, which sample walks over a graph to learn vector representations of vertices, and is foundational to the theory of Markov chains. Its long-run behaviour — recurrence, transience, and diffusion rate — depends on the dimensionality and structure of the underlying space.