论文标题
用于分支布朗运动的高斯粒子分布，具有不均匀的分支速率
A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate
论文作者
论文摘要
通过了解接受选择的人群演变的目标，我们考虑分支布朗尼运动，在该运动中，根据一维的布朗运动，颗粒独立移动，每个粒子可以分为二，或死亡，而出生率和死亡率之间的差异是粒子位置的线性函数。我们表明，在某些假设下，经过足够长的时间，颗粒位置的经验分布大约是高斯。这为生物学文献中的数学上有严格的理由提供了严格的理由，这表明随着时间的流逝，人群中个人的适应性水平像高斯行动波一样演变。
Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may either split into two or die, and the difference between the birth and death rates is a linear function of the position of the particle. We show that, under certain assumptions, after a sufficiently long time, the empirical distribution of the positions of the particles is approximately Gaussian. This provides mathematically rigorous justification for results in the biology literature indicating that the distribution of the fitness levels of individuals in a population over time evolves like a Gaussian traveling wave.
