Random walks

Imagine the following problem: a drunkard starts walking from a lampost taking $N$ steps of equal length in random directions: how far will the drunkard be from the lampost? This is the original formulation of the ``random walk'' problem, that can be generalized to more complex problems is physics, biology, chemistry and social sciences. We have seen an application to one dimensional integration in the previous section. Here we are going to study them in a more general context.