论文标题
复制器合并
The replicator coalescent
论文作者
论文摘要
我们考虑了一种随机模型，称为复制器融合，描述了$ k $不同类型的块的系统，该系统根据块类型进行成对合并，以$ c_ {i，j} $ block $ c_ {i，j} $ blocks $ i $ i $和$ j $ MERGE的块，导致单个类型$ i $的块。在多类型的环境中，复制器合并可以看作是金曼在多型环境中对金曼共同死亡链的概括，尽管没有可交换的分区结构。该名称源自我们从任意大量块发出的多类聚结合的瞬时动力学与所谓的“进化游戏理论”中所谓的复制器方程之间的瞬时动力学之间得出的。通过任意接近零的时间扩张时间，我们看到，最初，从无穷大降下时，复制器合并的表现就像对某个复制器方程的解决方案一样。此后，感受到了随机效应，并以多类死亡链的精神进化了过程。
We consider a stochastic model, called the replicator coalescent, describing a system of blocks of $k$ different types which undergo pairwise mergers at rates depending on the block types: with rate $C_{i,j}$ blocks of type $i$ and $j$ merge, resulting in a single block of type $i$. The replicator coalescent can be seen as generalisation of Kingman's coalescent death chain in a multi-type setting, although without an underpinning exchangeable partition structure. The name is derived from a remarkable connection we uncover between the instantaneous dynamics of this multi-type coalescent when issued from an arbitrarily large number of blocks, and the so-called replicator equations from evolutionary game theory. By dilating time arbitrarily close to zero, we see that initially, on coming down from infinity, the replicator coalescent behaves like the solution to a certain replicator equation. Thereafter, stochastic effects are felt and the process evolves more in the spirit of a multi-type death chain.
