UNIVERSALITY FOR CRITICAL KCM: FINITE NUMBER OF STABLE DIRECTIONS

• 成果类型: Article
• 署名作者: Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; Roma Tre University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1500
• 发表日期: 2021
• 页码: 2141-2174
• 关键词: bootstrap percolation; DYNAMICS; models

摘要

In this paper, we consider kinetically constrained models (KCM) on Z(2) 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 (Probab. Theory Related Fields 178 (2020) 289-326), Mareche 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 (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 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.