Spread of an infection on the zero range process
Spread of an infection on the zero range process
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零范围过程中感染的传播
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Teixeira
中科院分区：
文献类型：
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作者：
Rangel Baldasso;A. Teixeira
我们研究一种传染病在流动人口中的传播。环境演变为整数晶格上的零范围过程，从平衡状态开始。在时间0时，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。如果一个健康的粒子与一个受感染的粒子共用一个位点，它就会立即被感染。我们证明了感染波的锋面以正有限速度向右传播。作为证明这些结果的中心步骤，我们证明了零距离过程的时空解耦，这本身就很有趣。利用喷溅技术，我们得到了支撑距离足够远的轨迹空间函数相关性的估计。
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.