论文标题
$ k $ - 布朗连续树的模型
$k$-cut model for the Brownian Continuum Random Tree
论文作者
论文摘要
为了建模弹性网络的破坏，CAI，Holmgren，Devroye和Skerman在随机树上引入了$ K $ CUT模型，这是切割随机树的经典问题的扩展。 Berzunza，Cai和Holmgren后来证明，$ k $ cut模型中的削减总数隔离了Galton-Watson树的根 - Watson Tree具有有限的变化后代定律，并具有$ n $ nodes的条件，当将$ n $ nodes划分为$ n^{1-1/2k} $时，将其分配给了一些随机变量，以分配一些随机变量。我们在这里提供了限制随机变量的直接构造，该变量依赖于Aldous-Pitman的碎片化过程和确定性的时间变化。
To model the destruction of a resilient network, Cai, Holmgren, Devroye and Skerman introduced the $k$-cut model on a random tree, as an extension to the classic problem of cutting down random trees. Berzunza, Cai and Holmgren later proved that the total number of cuts in the $k$-cut model to isolate the root of a Galton--Watson tree with a finite-variance offspring law and conditioned to have $n$ nodes, when divided by $n^{1-1/2k}$, converges in distribution to some random variable defined on the Brownian CRT. We provide here a direct construction of the limit random variable, relying upon the Aldous-Pitman fragmentation process and a deterministic time change.
