We construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates proportional to their sums. The first construction, due to Aldous and Pitman, involves the components obtained by logging the Brownian continuum random tree (CRT) by a Poissonian rain on its skeleton as time increases. The second one, due to Bertoin, involves the excursions above its running infimum of a linear-drifted standard Brownian excursion as its drift decreases. Our main tool is the use of an exploration algorithm of the so-called cut-tree of the Brownian CRT, which is a tree that encodes the genealogy of the fragmentation of the CRT.

中文翻译：

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耦合 Bertoin 和 Aldous-Pitman 对添加剂成膜剂的表示

我们在标准添加剂聚结剂的两种看似非常不同的结构之间构建了耦合，它描述了质量成对合并的演化，速率与其总和成正比。第一个构造由 Aldous 和 Pitman 提出，涉及通过随着时间的增加通过泊松雨在其骨架上记录布朗连续随机树（CRT）而获得的组件。第二个由 Bertoin 提出，涉及当线性漂移标准布朗偏移减小时，其运行下确界之上的偏移。我们的主要工具是使用所谓的布朗 CRT 切割树的探索算法，该算法是对 CRT 碎片谱系进行编码的树。