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How to generate the tip of branching random walks evolved to large times
EPL ( IF 1.8 ) Pub Date : 2020-09-06 , DOI: 10.1209/0295-5075/131/40002
. Brunet 1 , A. D. Le 2 , A. H. Mueller 3 , S. Munier 2
Affiliation  

In a branching process, the number of particles increasesexponentially with time, which makes numerical simulations for large timesdifficult. In many applications, however, only the region close to the extremalparticles is relevant (the “tip”). We present a simple algorithmwhich allows to simulate a branching random walk in one dimension, keepingonly the particles that arrive within some distance of the rightmost particle ata predefined time T . The complexity of the algorithm growslinearly with T . We can furthermore choose to require that therealizations have their rightmost particle arbitrarily far on the right from itstypical position. We illustrate our algorithm by evaluating an observable forwhich no other practical method is known.

中文翻译:

如何产生分支随机游动的尖端进化到大范围

在分支过程中,粒子数随时间呈指数增长,这使得数值模拟的大时间变得困难。但是,在许多应用中,只有靠近极端颗粒的区域才是相关的(“尖端”)。我们提出了一种简单的算法,该算法可以模拟一维分支随机游动,仅将到达最右边粒子ata预定义时间T一定距离内的粒子保持在一定距离内。该算法的复杂度随着T线性增长。我们还可以选择要求实现的最右边粒子任意远离其典型位置。我们通过评估一个可观测值来说明我们的算法,对于该可观测值尚无其他实际方法可知。
更新日期:2020-09-08
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