通过Lévy型过程的偏移的永恒乘法合并编码，补充
The eternal multiplicative coalescent encoding via excursions of Lévy-type processes, with Supplement
摘要：
乘法合并是一个平均场马尔可夫过程，其中任何一对块体以与它们的质量的乘积成比例的速率合并。Aldous和Limic（1998）用三种不同的方式描述了乘法结合的每一个极端永恒版本，其中一种将其（边际）定律与某个Lévy型过程的过去最小值之上的有序偏移长度的定律相匹配。通过对Aldous（1997）和Aldous and Limic（1998）的广度优先行走结构的修改，以及Uribe（2007）论文中的一些新见解，这项工作解决了Aldous（1997）在Aldous and Limic（1998）更一般背景下的一个开放问题（3）。非正式地说，每一个永恒的版本都完全由它的Lévy型过程编码，与Aldous最初的直觉相反，乘法结合的时间确实对应于Léy型过程漂移的常数部分的线性增加。在Aldous（1997）的“标准乘法合并”背景下，这个结果首先由Armendáriz在2001年宣布，而它的第一个公开证明是由于Broutin和Marckert（2016），他们同时解释了多余（或剩余）边计数的过程。
英文摘要：
The multiplicative coalescent is a mean-field Markov process in which any pair of blocks coalesces at rate proportional to the product of their masses. In Aldous and Limic (1998) each extreme eternal version of the multiplicative coalescent was described in three different ways, one of which matched its (marginal) law to that of the ordered excursion lengths above past minima of a certain Lévy-type process. Using a modification of the breadth-first-walk construction from Aldous (1997) and Aldous and Limic (1998), and some new insight from the thesis by Uribe (2007), this work settles an open problem (3) from Aldous (1997) in the more general context of Aldous and Limic (1998). Informally speaking, each eternal version is entirely encoded by its Lévy-type process, and contrary to Aldous' original intuition, the time for the multiplicative coalescent does correspond to the linear increase in the constant part of the drift of the Lé}y-type process. In the "standard multiplicative coalescent" context of Aldous (1997), this result was first announced by Armendáriz in 2001, while its first published proof is due to Broutin and Marckert (2016), who simultaneously account for the process of excess (or surplus) edge counts.
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