论文标题
从无限界面开始的连续空间和生长特性中的测量值增长过程
Measure-valued growth processes in continuous space and growth properties starting from an infinite interface
论文作者
论文摘要
在Louvet中引入的K-Parent和无限的空间空间lambda-Fleming Viot过程（或SLFV）（2023年），形成了用于空间扩展人群的随机模型家族。这些过程类似于经典伊甸园增长模型的连续空间版本（但在k是有限时允许的占用区域的本地回溯），同时与编码祖先的双重过程相关联。 在本文中，我们关注1型个人所占据的区域的生长特性（类型0编码空白空间的单位）。为此，我们首先定义了我们将使用的数量来量化占用区域的生长速度。使用相关的双重过程和与第一步渗透问题的比较，我们表明，无限父母SLFV中占用区域的生长是线性的。由于占用区域的局部回溯可能，我们为K-Parent SLFV获得的结果略有弱。它给定位置在时间t上占据的概率给出了上限，这也表明，K-Parent SLFV的生长在时间上是线性的。我们使用数值模拟来近似无限父母SLFV的生长速度，并且我们观察到，由于特征前的前动力学，实际速度可能高于简单第一瞬间计算的速度。
The k-parent and infinite-parent spatial Lambda-Fleming Viot processes (or SLFV), introduced in Louvet (2023), form a family of stochastic models for spatially expanding populations. These processes are akin to a continuous-space version of the classical Eden growth model (but with local backtracking of the occupied area allowed when k is finite), while being associated to a dual process encoding ancestry. In this article, we focus on the growth properties of the area occupied by individuals of type 1 (type 0 encoding units of empty space). To do so, we first define the quantities that we shall use to quantify the speed of growth of the occupied area. Using the associated dual process and a comparison with a first-passage percolation problem, we show that the growth of the occupied region in the infinite-parent SLFV is linear in time. Because of the possibility of local backtracking of the occupied area, the result we obtain for the k-parent SLFV is slightly weaker. It gives an upper bound on the probability that a given location is occupied at time t, which also shows that growth in the k-parent SLFV is linear in time. We use numerical simulations to approximate the growth speed for the infinite-parent SLFV, and we observe that the actual speed may be higher than the speed expected from simple first-moment calculations due to the characteristic front dynamics.
