• DOI:10.1007/s00440-020-00976-9
• Corpus ID: 204575965

Universality for critical KCM: infinite number of stable directions

@article{Hartarsky2020UniversalityFC,
  title={Universality for critical KCM: infinite number of stable directions},
  author={Ivailo Hartarsky and Laure Marêché and Cristina Toninelli},
  journal={Probability Theory and Related Fields},
  year={2020},
  pages={1-38}
}

• Ivailo Hartarsky, Laure Marêché, C. Toninelli
• Published 19 April 2019
• Mathematics
• Probability Theory and Related Fields

Kinetically constrained models (KCM) are reversible interacting particle systems on $${{\mathbb {Z}}} ^d$$ Z d with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with random initial state known as $${{\mathscr {U}}}$$ U -bootstrap percolation. KCM have an interest in their own right, owing to their use for modelling the liquid-glass transition in condensed matter physics. In two dimensions there are three classes of models with qualitatively different scaling of the infection time of the origin as the density of infected sites vanishes. Here we study in full generality the class termed ‘critical’. Together with the companion paper by Hartarsky et al. (Universality for critical KCM: finite number of stable directions. arXiv e-prints arXiv:1910.06782 , 2019) we establish the universality classes of critical KCM and determine within each class the critical exponent of the infection time as well as of the spectral gap. In this work we prove that for critical models with an infinite number of stable directions this exponent is twice the one of their bootstrap percolation counterpart. This is due to the occurrence of ‘energy barriers’, which determine the dominant behaviour for these KCM but which do not matter for the monotone bootstrap dynamics. Our result confirms the conjecture of Martinelli et al. (Commun Math Phys 369(2):761–809. https://doi.org/10.1007/s00220-018-3280-z , 2019), who proved a matching upper bound.