Universality for critical KCM: infinite number of stable directions

In this paper we consider kinetically constrained models (KCM) on Z2 with general update families U . For U belonging to the so-called “critical class” our focus is on the divergence of the infection time of the origin for the equilibrium process as the density of the facilitating sites vanishes. In a recent paper [14] Marêché and two of the present authors proved that if U has an infinite number of “stable directions,” then on a doubly logarithmic scale the above divergence is twice the one in the corresponding U-bootstrap percolation. Here we prove instead that, contrary to previous conjectures [20], in the complementary case the two divergences are the same. In particular, we establish the full universality partition for critical U . The main novel contribution is the identification of the leading mechanism governing the motion of infected critical droplets. It consists of a peculiar hierarchical combination of mesoscopic East-like motions.