Random walks

Random walks are a mathematical model that is used to describe a path that is given by a succession of random steps, which, depending on the system that we want to describe, may have a certain number of degrees of freedom or direction. The term random walk was introduced by Karl Pearson in 1905. In a random walk, each step has a random direction and possibly also a random dimension. It represents a theoretical model to describe any random process through the evolution of known quantities that follow a precise statistical distribution. Physically speaking, the path that we are going to draw over time will not necessarily describe a real motion, but rather indicate more generally the evolution of features over time. This means that random walks find applications in physics, chemistry, and biology, but also in other fields, such as computer science, economics, and sociology.