A Wiener process is the scaling limit of random walk in dimension 1. This means that if you take a random walk with very small steps, you get an approximation to a Wiener process (and, less accurately, to Brownian motion). To be more precise, if the step size is ε, one needs to take a walk of length "L"/ε2 to approximate a Wiener length of "L". As the step size tends to 0 (and the number of steps increases proportionally), random walk converges to a Wiener process in an appropriate sense. Formally, if "B" is the space of all paths of length "L" with the maximum topology, and if "M" is the space of measure over "B" with the norm topology, then the convergence is in the space "M". Similarly, a Wiener process in several dimensions is the scaling limit of random walk in the same number of dimensions.