We consider the model of random trees introduced by Devroye, the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation on those trees and obtain a precise weak limit theorem for the sizes of the largest clusters. We also show that the approach developed in this work may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we also study the case of d-regular trees.

中文翻译：

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随机分裂树上超临界渗流的簇大小渐近分布

我们考虑 Devroye 引入的随机树模型，即所谓的随机分裂树。该模型包含许多重要的随机算法和数据结构。然后，我们对这些树执行超临界伯努利键渗透，并获得最大星团大小的精确弱极限定理。我们还表明，这项工作中开发的方法可能有助于研究其他具有对数高度的树的渗透，例如，我们还研究了d正则树的情况。