论文标题
感染传播的局部生存
Local survival of spread of infection among biased random walks
论文作者
论文摘要
我们研究感染在$ \ mathbb {z}^{d} $上散布的随机步行之间传播。随机步行独立移动，并以零时间放置感染粒子。当颗粒共享同一部位并且没有恢复时，感染会立即传播。如果颗粒的初始密度足够小，则感染的云在随机行走的偏见方向上传播，这意味着感染无法局部生存。当密度较大时，感染扩散到整个$ \ mathbb {z}^{d} $。证明依赖于两种不同的技术。对于小密度情况，我们通过族谱路径对感染云的描述进行描述，而大密度的情况依赖于重新归一化的方案。
We study infection spread among biased random walks on $\mathbb{Z}^{d}$. The random walks move independently and an infected particle is placed at the origin at time zero. Infection spreads instantaneously when particles share the same site and there is no recovery. If the initial density of particles is small enough, the infected cloud travels in the direction of the bias of the random walks, implying that the infection does not survive locally. When the density is large, the infection spreads to the whole $\mathbb{Z}^{d}$. The proofs rely on two different techniques. For the small density case, we use a description of the infected cloud through genealogical paths, while the large density case relies on a renormalization scheme.
