论文标题
亚伯网络的基本增强：连续性和统一的严格单调性
Essential enhancements in Abelian networks: continuity and uniform strict monotonicity
论文作者
论文摘要
我们证明，在广泛的一般性中，激活的随机步行模型的临界曲线是停用速率的连续函数，并且我们在其斜率上提供了一个界限，相对于图形的选择，这是均匀的。此外，我们为广泛的“增加”事件的概率得出了严格的单调性能，从而扩展了Rolla和Sidoravicius的先前结果（2012年）。我们的证明方法具有独立的兴趣，可以被视为在阿贝尔网络框架内引入“基本增强”技术的重新制定（用于渗透的技术）。
We prove that in wide generality the critical curve of the activated random walk model is a continuous function of the deactivation rate, and we provide a bound on its slope which is uniform with respect to the choice of the graph. Moreover, we derive strict monotonicity properties for the probability of a wide class of `increasing' events,extending previous results of Rolla and Sidoravicius (2012). Our proof method is of independent interest and can be viewed as a reformulation of the `essential enhancements' technique -- which was introduced for percolation -- in the framework of Abelian networks.
