A Markov chain approach to renormalization group transformations

► An explicit characterization of the decimation effect on the Ising Hamiltonian is achieved through the Markov-Gibbs equivalence. ► The decimation flow on the Ising Hamiltonian is translated into a flow on the associated Markov chains. ► Two different proofs of the universality conjecture are presented. ► This work has implications for more general renormalization group transformations.