标题： 随机性对无穷父代SLFV过程增长的影响 显示英文标题

标题： Effect of stochasticity on the growth of the infty-parent SLFV process

摘要： 我们探讨了不同形式的随机性对称为$\infty$-parent spatial$\Lambda$-Fleming Viot 过程的随机生长模型扩张动力学的影响。 该过程属于空间连续体中的种群遗传学过程，最近被引入以研究空间扩张种群中遗传多样性的演化。 其随机繁殖动力学产生了一个丰富的生长结构，首次理论结果已在此基础上获得。 在本文中，我们进一步通过两种互补的方法探索这一生长动力学：对前沿生长的简化模型进行分析研究，以及基于模拟的研究。 我们表明，观察到的扩张速度是繁殖事件形状、时间和位置的随机性相互作用的结果，每种形式的随机性都是必要但不足以解释扩张动力学。 我们还确定了前沿和扩张主体的到达时间方差的不同标度区域。 此外，我们获得了前沿波动的标度结果，这些结果指向前沿界面属于KPZ普适类。 显示英文摘要

摘要： We explore the impact of different forms of stochasticity on the expansion dynamics of a stochastic growth model called the $\infty$-parent spatial $\Lambda$-Fleming Viot process. This process belongs to a family of population genetics processes in a spatial continuum, and was recently introduced to study the evolution of genetic diversity in spatially expanding populations. Its stochastic reproduction dynamics gives rise to a rich growth structure, on which first theoretical results were obtained. In this paper, we further explore this growth dynamics using two complementary approaches: an analytical study of a simplified model for growth at the front edge, and a simulation-based study. We show that the observed expansion speed is the result of the interplay of stochasticity in shapes, timings and locations of reproduction events, each form of stochasticity being necessary but not sufficient to explain the expansion dynamics. We also identify distinctive scaling regimes for the variance of hitting times by the front and the bulk of the expansion. Moreover, we obtain results on the scaling of the front fluctuations, which point towards the front interface belonging to the KPZ universality class.