论文标题
在随机拆分树上的超临界渗透的集群大小的渐近分布
The asymptotic distribution of cluster sizes for supercritical percolation on random split trees
论文作者
论文摘要
我们考虑Devroye（1999）引入的随机树的模型，即所谓的随机拆分树。该模型包括许多重要的随机算法和数据结构。然后，我们对这些树木进行超临界的Bernoulli键 - 渗透，并为最大簇的大小获得精确的弱极限定理。我们还表明，这项工作中开发的方法可能有助于研究其他对数高度的树木类别的渗透，我们还研究了$ d $ regratular的树木。
We consider the model of random trees introduced by Devroye (1999), 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 study also the case of $d$-regular trees.
