A new combinatorial representation of the additive coalescent
A new combinatorial representation of the additive coalescent
复制标题
添加剂成膜助剂的新组合表示
DOI：
10.1002/rsa.20775
复制
发表时间：
2019
影响因子：
1
通讯作者：
Minmin Wang
中科院分区：
文献类型：
--
作者：
J. Marckert;Minmin Wang
从n个粒子开始的标准可加聚结是一个马尔可夫过程，它具有几个组合表示，一个由皮特曼作为聚结森林的过程，一个由Chassaing和Louchard作为停车方案中的块大小。在联合森林表示中，边被连续地添加在随机节点和随机根之间。在本文中，我们研究了另一种结构，而不是，根之间添加边缘。这种构造在簇大小方面诱导了完全相同的过程，同时，它允许我们与其他组合和概率模型建立许多新的联系：大小偏置渗透，树中的停车方案，增加树，树的随机切割。所涉及的组合对象的多样性证明了我们对这种构造的兴趣。
The standard additive coalescent starting with n particles is a Markov process which owns several combinatorial representations, one by Pitman as a process of coalescent forests, and one by Chassaing and Louchard as the block sizes in a parking scheme. In the coalescent forest representation, edges are added successively between a random node and a random root. In this paper, we investigate an alternative construction by, instead, adding edges between roots. This construction induces exactly the same process in terms of cluster sizes, meanwhile, it allows us to make numerous new connections with other combinatorial and probabilistic models: size biased percolation, parking scheme in a tree, increasing trees, random cuts of trees. The variety of the combinatorial objects involved justifies our interest in this construction.