论文标题
在非局部相互作用粒子的离散波中的随机漂移
Stochastic drift in discrete waves of non-locally interacting-particles
论文作者
论文摘要
在本文中，我们研究了在晶格上经历二阶非本地相互作用的$ n $颗粒的广义模型。我们的结果在许多研究领域都有应用，包括迁移的建模，信息动态和穆勒的棘轮 - 不可逆转的人群中有害突变的不可逆转积累。令人惊讶的是，观察到该模型的数值模拟即使对于较大的人口大小，也可以显着偏离其平均场近似值。我们表明，确定性和随机溶液之间的分歧源于有限大小的效应，这些效应改变了传播速度并导致波浪的位置波动。这些效果表明异常衰减为$（\ log n）^{ - 2} $和$（\ log n）^{ - 3} $，比通常的$ n^{ - 1/2} $ factor慢得多。我们的结果表明，穆勒棘轮中有害突变的积累，人口中的意识丧失可能比相应的确定性模型所预测的要快得多。我们模型的一般适用性表明，这种意外的缩放可能在广泛的现实应用程序中很重要。
In this paper, we investigate a generalised model of $N$ particles undergoing second-order non-local interactions on a lattice. Our results have applications across many research areas, including the modelling of migration, information dynamics and Muller's ratchet -- the irreversible accumulation of deleterious mutations in an evolving population. Strikingly, numerical simulations of the model are observed to deviate significantly from its mean-field approximation even for large population sizes. We show that the disagreement between deterministic and stochastic solutions stems from finite-size effects that change the propagation speed and cause the position of the wave to fluctuate. These effects are shown to decay anomalously as $(\log N)^{-2}$ and $(\log N)^{-3}$, respectively -- much slower than the usual $N^{-1/2}$ factor. Our results suggest that the accumulation of deleterious mutations in a Muller's ratchet and the loss of awareness in a population may occur much faster than predicted by the corresponding deterministic models. The general applicability of our model suggests that this unexpected scaling could be important in a wide range of real-world applications.
