We establish the rate of weak convergence in the fractional step method for the Arratia flow in terms of the Wasserstein distance between the images of the Lebesgue measure under the action of the flow. We introduce finite-dimensional densities that describe sequences of collisions in the Arratia flow and derive an explicit expression for them. For the discretized initial interval, we also discuss the convergence of the corresponding approximations of the point measure associated with the Arratia flow in terms of these densities.

中文翻译：

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利用分数步法和初始间隔离散化的布朗网相关点测度的逼近

我们根据流作用下Lebesgue测度的图像之间的Wasserstein距离，建立了Arratia流的分数阶跃方法中的弱收敛速率。我们引入了描述Arratia流中碰撞序列的有限维密度，并为它们导出了一个明确的表达式。对于离散化的初始间隔，我们还讨论了根据这些密度与Arratia流相关的点测度的相应近似值的收敛性。