"Renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology - art. no. 084026

We study the "renormalization group action" induced by cycles of cosmic exp ansion and contraction, within the context of a family of stochastic dynami cal laws for causal sets derived earlier. We find a line of fixed points co rresponding to the dynamics of transitive percolation, and we prove that th ere exist no other fixed points and no cycles of length greater than or equ al to2. We also identify an extensive ''basin of attraction" of the fixed p oints but find that it does not exhaust the full parameter space. Neverthel ess, we conjecture that every trajectory is drawn toward the fixed point se t in a suitably weakened sense.