论文标题
如何产生分支随机步行的尖端，发展到大时
How to generate the tip of branching random walks evolved to large times
论文作者
论文摘要
在分支过程中，粒子的数量随时间呈指数增加，这使得在大时的数值模拟变得困难。但是，在许多应用中，只有接近极端颗粒的区域是相关的（“尖端”）。我们提出了一种简单的算法，该算法允许在一个维度上模拟分支随机行走，仅在预定义的时间$ t $的情况下将到达最右边粒子的距离内的粒子保持一定距离。算法的复杂性随$ t $线性增长。我们还可以选择要求实现其最右边的粒子与典型位置任意远处。我们通过评估可观察到的其他实际方法的可观察方法来说明我们的算法。
In a branching process, the number of particles increases exponentially with time, which makes numerical simulations for large times difficult. In many applications, however, only the region close to the extremal particles is relevant (the "tip"). We present a simple algorithm which allows to simulate a branching random walk in one dimension, keeping only the particles that arrive within some distance of the rightmost particle at a predefined time $T$. The complexity of the algorithm grows linearly with $T$. We can furthermore choose to require that the realizations have their rightmost particle arbitrarily far on the right from its typical position. We illustrate our algorithm by evaluating an observable for which no other practical method is known.
