Homomorphism to R generated by abstract length functions: a dynamical construction - Gastão Bettencourt (2022)
Erschler and Karlsson in [5] construct a homomorphism of a finitely generated group G to R using a random walk approach. Central to their construction were the word length$\ell$ and a well behaved measure $μ$ on G. In this note we define a class of abstract length functions and prove that Erschler and Karlsson construction can also be applied to this class.