非单调种群模型中的线性传播速度
Linear spreading speed in non-monotone population models
浏览论文内容
中文总结 AI 辅助
研究一类离散时间有限范围相互作用粒子系统在\(\mathbb{Z}\)上的线性传播速度，通过与超临界定向渗流耦合及‘移位耦合’方法，在不假设单调性下建立定理，如离散时间分支湮灭随机游走符合框架并展现线性传播速度。
中文摘要 AI 辅助
对于一类广泛的离散时间、有限范围相互作用的粒子系统在\(\mathbb{Z}\)上，我们在生存事件上建立了线性传播速度和一维形状定理，不假设动力学的单调性或吸引力。方法要求系统在粗粒度格上允许与超临界定向渗流耦合。核心技术步骤是通过‘移位耦合’获得击中时间的近似次可加性，以弥补缺乏单调性。具体应用表明离散时间分支湮灭随机游走符合此框架并具有线性传播速度。
英文摘要
For a broad class of discrete-time, finite-range interacting particle systems on $\mathbb{Z}$, we establish a linear spreading speed and a one-dimensional shape theorem on the event of survival, without assuming monotonicity or attractiveness of the dynamics. The method requires that the system admits a coupling with supercritical oriented percolation on a coarse-grained lattice. The central technical step is an approximate subadditivity property for the hitting times, obtained through a `shifted coupling' that compensates for the absence of monotonicity. As a concrete application, we show that a discrete-time branching annihilating random walk fits into this framework, and consequently exhibits a linear spreading speed.
