Some large deviations in Kingman's coalescent

@article{Depperschmidt2013SomeLD,
  title={Some large deviations in Kingman's coalescent},
  author={Andrej Depperschmidt and Peter Pfaffelhuber and Annika Scheuringer},
  journal={arXiv: Probability},
  year={2013}
}
Kingman's coalescent is a random tree that arises from classical population genetic models such as the Moran model. The individuals alive in these models correspond to the leaves in the tree and the following two laws of large numbers concerning the structure of the tree-top are well-known: (i) The (shortest) distance, denoted by $T_n$, from the tree-top to the level when there are $n$ lines in the tree satisfies $nT_n \xrightarrow{n\to\infty} 2$ almost surely; (ii) At time $T_n$, the… 

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