论文标题
$λ$ -Coalescents的概率方面和进化
Probabilistic aspects of $Λ$-coalescents in equilibrium and in evolution
论文作者
论文摘要
我们提出了近似方法，这些方法在无尘的情况下和具有灰尘成分的情况下，导致了$λ$ - 粉丝的功能的大量和波动结果。我们的重点是树长（或总分支长度）和总外部分支长度，以及最新共同祖先和最后合并的大小的时间。在第二部分中，我们讨论了不断发展的结合体。对于某些β-钙化，我们分析了适当的时间尺度的一类功能的波动。最终，我们回顾了古夫勒（Gufler）关于在lookdown空间中不断发展的$λ$ coalescents代表的结果。
We present approximation methods which lead to law of large numbers and fluctuation results for functionals of $Λ$-coalescents, both in the dust-free case and in the case with a dust component. Our focus is on the tree length (or total branch length) and the total external branch length, as well as the time to the most recent common ancestor and the size of the last merger. In the second part we discuss evolving coalescents. For certain Beta-coalescents we analyse fluctuations of a class of functionals in appropriate time scales. Finally we review results of Gufler on the representation of evolving $Λ$-coalescents in terms of the lookdown space.
