论文标题
从平衡的动力学约束模型
Kinetically constrained models out of equilibrium
论文作者
论文摘要
我们研究了在任意维度和平衡中的动力学约束模型的整个类别，在均衡度量中促进站点的密度$ q $（但不一定在初始措施中）接近$ 1 $。对于这些模型，我们在有限的边界条件下建立了无限体积和线性时间前的指数收敛。我们的结果是所谓关键类别中任何模型的第一个不平衡结果，该模型由我们的治疗中的整体涵盖，包括例如Fredrickson-Andersen 2-Spin促进了模型。此外，它们概括，统一，有时简化了该领域的几项以前的作品。作为副产品，我们在扰动的细胞自动机的上部不变轨迹以及亚临界引导渗透模型中最终感染的位点的集合中恢复并概括了指数尾部。我们的方法通过研究合作接触过程，最后一段渗透，Toom轮廓以及接触过程和动力学约束模型之间非常方便的耦合。
We study the full class of kinetically constrained models in arbitrary dimension and out of equilibrium, in the regime where the density $q$ of facilitating sites in the equilibrium measure (but not necessarily in the initial measure) is close to $1$. For these models, we establish exponential convergence to equilibrium in infinite volume and linear time precutoff in finite volume with appropriate boundary condition. Our results are the first out-of-equilibrium results that hold for any model in the so-called critical class, which is covered in its entirety by our treatment, including e.g. the Fredrickson-Andersen 2-spin facilitated model. In addition, they generalise, unify and sometimes simplify several previous works in the field. As byproduct, we recover and generalise exponential tails for the connected component of the origin in the upper invariant trajectory of perturbed cellular automata and in the set of eventually infected sites in subcritical bootstrap percolation models. Our approach goes through the study of cooperative contact processes, last passage percolation, Toom contours, as well as a very convenient coupling between contact processes and kinetically constrained models.
