We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous variant, we prove that the process can reach infinity in finite time i.e., explode. In particular, we prove that explosions occur almost surely on regular trees as well as oriented and unoriented two-dimensional integer lattices with sufficiently many particles per site. The oriented case requires an additional hypothesis about the existence and value of a certain critical exponent. We further prove that the process with one particle per site expands at a superlinear rate on integer lattices of any dimension. Some arguments use connections to critical first passage percolation, including a new result about the existence of an infinite path with finite passage time on the oriented two-dimensional lattice.

中文翻译：

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临界渗透和 A+B$$\rightarrow $$2A 动力学

我们研究了一个相互作用的粒子系统，在该系统中，移动的粒子会激活由临界键渗透的组件连接的休眠粒子。针对 Beckman、Dinan、Durrett、Huo 和 Junge 对连续变体的猜想，我们证明了该过程可以在有限时间内达到无穷大，即爆炸。特别是，我们证明爆炸几乎肯定会发生在规则树以及每个位置有足够多粒子的定向和非定向二维整数格子上。定向案例需要关于某个临界指数的存在和价值的附加假设。我们进一步证明，每个位点一个粒子的过程在任何维度的整数晶格上以超线性速率扩展。一些论点使用与关键的第一段渗透的联系，