论文标题
连续时间青蛙模型的线性和超线性扩展
Linear and superlinear spread for continuous-time frog model
论文作者
论文摘要
考虑$ \ Mathbb {z} ^d $上的随机增长模型。从其他地方的原点和睡眠颗粒开始。 $ x \ in \ mathbb {z} ^d $ in $ x \ in $ x \ in $ h（x）$的初始数量，其中$η（x）$是根据$μ$分配的独立随机变量。活跃的颗粒执行简单的连续随机步行，而睡眠颗粒保持固定，直到活跃粒子首次到达其位置。到达后，现场的所有睡眠颗粒都立即激活，并根据自己的简单随机步行开始移动。本文的目的是给出$μ$的条件，根据该过程，该过程的传播是线性或比线性更快的。证明取决于与各种渗滤模型的比较。
Consider a stochastic growth model on $\mathbb{Z} ^d$. Start with some active particle at the origin and sleeping particles elsewhere. The initial number of particles at $x \in \mathbb{Z} ^d$ is $η(x)$, where $η(x)$ are independent random variables distributed according to $μ$. Active particles perform a simple continuous-time random walk while sleeping particles stay put until the first arrival of an active particle to their location. Upon the arrival all sleeping particles at the site activate at once and start moving according to their own simple random walks. The aim of this paper is to give conditions on $μ$ under which the spread of the process is linear or faster than linear. The proofs rely on comparison to various percolation models.
