This distribution (denote it by ) is called the scaling limit of loop-erased random walk.

This suggests that the scaling limit should have Hausdorff dimension between and 5/3 almost surely.

The double scaling limit is often applied to matrix models, string theory, and other theories to obtain their simplified versions.

This case also arises in the scaling limit of critical percolation on the triangular lattice.

This presupposes the existence of a scaling limit.

The Wiener process can be constructed as the scaling limit of a random walk, or other discrete-time stochastic processes with stationary independent increments.

The perturbative treatment becomes exact in the double scaling limit .

Indeed, according to Donsker's theorem, the discrete random walk would, in the scaling limit, approach the true Brownian motion.

Now, take the scaling limit as the string scale goes to zero with the string coupling kept fixed.

Systems display universality in a scaling limit, when a large number of interacting parts come together.