Intermediate asymptotics and renormalization group theory

The principles of the renormalization group (RG) are presented pedagogically from the point of view of intermediate asymptotics (IA), which is familiar to hydrodynamicists and applied mathematicians. To demonstrate the equivalence of RG and IA approaches, a typical statistical mechanical problem, conventionally studied by the renormalized perturbation approach, is reconsidered from the IA point of view, and renormalized perturbation theory is applied to a partial differential equation conventionally studied by IA. This example is important because it is an explicit demonstration that the RG can be applied to partial differential equations without adding a noise source. We suggest that the ideas explained in this article may be applicable to the Navier-Stokes equation.