Continuum limit

An animated example of a Brownian motion-like random walk on a torus. In the scaling limit, random walk approaches the Wiener process according to Donsker's theorem.

In mathematical physics and mathematics, the continuum limit or scaling limit of a lattice model characterizes its behaviour in the limit as the lattice spacing goes to zero. It is often useful to use lattice models to approximate real-world processes, such as Brownian motion. Indeed, according to Donsker's theorem, the discrete random walk would, in the scaling limit, approach the true Brownian motion.