Abstract
In this paper, we consider kinetically constrained models (KCM) on with general update families . For 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 (Probab. Theory Related Fields 178 (2020) 289–326), Marêché and two of the present authors proved that if has an infinite number of “stable directions,” then on a doubly logarithmic scale the above divergence is twice the one in the corresponding -bootstrap percolation.
Here, we prove instead that, contrary to previous conjectures (Comm. Math. Phys. 369 (2019) 761–809), in the complementary case the two divergences are the same. In particular, we establish the full universality partition for critical . 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.
Funding Statement
The authors were supported by ERC Starting Grant 680275 “MALIG”. The second author was supported by PRIN 20155PAWZB “Large Scale Random Structures.” The third author was supported by ANR-15-CE40-0020-01.
Acknowledgment
We wish to thank Laure Marêché for many enlightening discussions concerning universality for -KCM.
Citation
Ivailo Hartarsky. Fabio Martinelli. Cristina Toninelli. "Universality for critical KCM: Finite number of stable directions." Ann. Probab. 49 (5) 2141 - 2174, September 2021. https://doi.org/10.1214/20-AOP1500
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