论文标题
随机递归度量空间的深度
Depths in random recursive metric spaces
论文作者
论文摘要
作为随机递归树和优先附着树的概括，我们考虑随机递归度量空间。这些空间是由随机块构造的，每个块都是一个设有概率度量的公制空间，其中包含一个称为钩子的标记点，并分配了一个重量。随机递归度量空间配备了一个概率度量，由分配给其组成块的概率度量的加权总和组成。在随机递归度量空间的生长的每个步骤中，根据装备的概率度量随机选择一个称为闩锁的点，并通过将新块随机选择一个新块，并通过将块的闩锁和块的钩子连接在一起。我们使用Martingale理论来证明大量法律和插入深度的中心限制定理。从主钩到所选闩锁的距离。我们还将结果应用于随机树，挂钩网络以及从线段构建的连续空间的进一步概括。
As a generalization of random recursive trees and preferential attachment trees, we consider random recursive metric spaces. These spaces are constructed from random blocks, each a metric space equipped with a probability measure, containing a labelled point called a hook, and assigned a weight. Random recursive metric spaces are equipped with a probability measure made up of a weighted sum of the probability measures assigned to its constituent blocks. At each step in the growth of a random recursive metric space, a point called a latch is chosen at random according to the equipped probability measure and a new block is chosen at random and attached to the space by joining together the latch and the hook of the block. We use martingale theory to prove a law of large numbers and a central limit theorem for the insertion depth; the distance from the master hook to the latch chosen. We also apply our results to further generalizations of random trees, hooking networks, and continuous spaces constructed from line segments.
