论文标题
生长液滴的关键长度
The critical length for growing a droplet
论文作者
论文摘要
在许多相互作用的粒子系统中，人们认为对平衡的放松是通过“液滴”的生长发生的，这是确定出现此类液滴的临界长度的根本重要性。在本文中，我们构建了一种在任意有限范围单调单调蜂窝自动机中在$ d $维晶格上生长的机制。我们的主要应用是对渗透的关键概率的上限，该概率尖锐到指数中的恒定因素。我们的方法还提供了几种至关重要的工具，我们期望将这些工具应用于其他相互作用的粒子系统，例如在$ \ Mathbb {z}^d $上的动力约束旋转模型。 这是三篇论文之一，共同确认了Bollobás，Duminil-Copin，Morris和Smith的普遍性。
In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper we construct a mechanism for the growth of droplets in an arbitrary finite-range monotone cellular automaton on a $d$-dimensional lattice. Our main application is an upper bound on the critical probability for percolation that is sharp up to a constant factor in the exponent. Our method also provides several crucial tools that we expect to have applications to other interacting particle systems, such as kinetically constrained spin models on $\mathbb{Z}^d$. This is one of three papers that together confirm the Universality Conjecture of Bollobás, Duminil-Copin, Morris and Smith.
