We study the “renormalization group action” induced by cycles of cosmic expansion and contraction, within the context of a family of stochastic dynamical laws for causal sets derived earlier. We find a line of fixed points corresponding to the dynamics of transitive percolation, and we prove that there exist no other fixed points and no cycles of length $>~2.$ We also identify an extensive “basin of attraction” of the fixed points but find that it does not exhaust the full parameter space. Nevertheless, we conjecture that every trajectory is drawn toward the fixed point set in a suitably weakened sense.

• Received 18 September 2000

DOI:https://doi.org/10.1103/PhysRevD.63.084026