标题： 线性上激活随机游走的超可加性和密度猜想的新证明 显示英文标题

标题： A new proof of superadditivity and of the density conjecture for Activated Random Walks on the line

摘要： 在两项最近的研究中，Hoffman、Johnson 和 Junge 证明了在一维激活随机游走模型中密度猜想、曲棍球棒猜想和球体猜想，展示了该模型中几种不同临界密度定义之间的等价性。这建立了一种自组织临界性，最初是针对阿贝尔沙堆模型预测的。他们的证明使用了与具有超加性的渗流过程的比较。我们在此提供这些猜想的不同证明，基于我们直接为激活随机游走建立的新超加性性质，而不依赖于渗流过程。这种更基础的方法得到的界限不如 Hoffman、Johnson 和 Junge 开发的渗流技术精确，但它可能为超越一维设置开辟新的前景。 显示英文摘要

摘要： In two recent works, Hoffman, Johnson and Junge proved the density conjecture, the hockey stick conjecture and the ball conjecture for Activated Random Walks in dimension one, showing an equality between several different definitions of the critical density of the model. This establishes a kind of self-organized criticality, which was originally predicted for the Abelian Sandpile Model. Their proof uses a comparison with a percolation process, which exhibits superadditivity. We present here a different proof of these conjectures, based on a new superadditivity property that we establish directly for Activated Random Walks, without relying on a percolation process. This more elementary approach yields less precise bounds than the percolation technology developed by Hoffman, Johnson and Junge, but it might open new perspectives to go beyond the one-dimensional setting.