Abstract

Despite the close connection between the central limit theorem and renormalization group (RG) methods, the latter should be considered fundamentally distinct from the kind of probabilistic framework associated with statistical mechanics, especially the notion of averaging. The mathematics of RG is grounded in dynamical systems theory rather than probability, which raises important issues with respect to the way RG generates explanations of physical phenomena. I explore these differences and show why RG methods should be considered not just calculational tools but the basis for a physical understanding of complex systems in terms of structural properties and relations