零范围进程上的感染传播
Spread of an infection on the zero range process
摘要：
我们研究的是在流动人群中传染病的传播。环境演化为整数格上的零程过程，从平衡开始。在零时刻，受感染的粒子集由负轴上的粒子组成，而原点右侧的粒子被认为是健康的。如果健康的粒子与被感染的粒子共享一个位点，那么它会立即被感染。我们证明了感染波的波前以正的有限速度向右传播。作为证明这些结果的一个中心步骤，我们证明了一个空时解耦的零程过程，这是有趣的本身。使用喷洒技术，我们得到的支持是足够远的轨迹空间的函数的相关性的估计。
英文摘要：
We study the spread of an infection on top of a moving population. The environment evolves as a zero range process on the integer lattice starting in equilibrium. At time zero, the set of infected particles is composed by those which are on the negative axis, while particles at the right of the origin are considered healthy. A healthy particle immediately becomes infected if it shares a site with an infected particle. We prove that the front of the infection wave travels to the right with positive and finite velocity. As a central step in the proof of these results, we prove a space-time decoupling for the zero range process which is interesting on its own. Using a sprinkling technique, we derive an estimate on the correlation of functions of the space of trajectories whose supports are sufficiently far away.
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