The occurrence of renormalization ideas in dynamical systems, while having a similar formalism to the more directly physical methodologies in statistical physics, has not been unambiguously connected to this statistical physics context. Broadly speaking, renormalization in dynamical systems tends to arise from induced return maps to some set, whereas renormalization in statistical physics relates to some “coarse-graining” (block-spin renormalization) of a collection of random variables. In this talk, I will discuss a possible direction of connection between these two settings by way of discussing the Bartholdi-Kaimanovich-Virag transformation (“Schur renormalization”) of random walks on self-similar groups. While this idea shows promise, I will demonstrate that in the most direct reduction of renormalization to this context, the two renormalization strategies (return maps and block spin) are distinct.