Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering the Brownian Coalescent Point Process from the Kingman
  Coalescent by Conditional Sampling   We consider a continuous population whose dynamics is described by the
standard stationary Fleming-Viot process, so that the genealogy of $n$
uniformly sampled individuals is distributed as the Kingman $n$-coalescent. In
this note, we study some genealogical properties of this population when the
sample is conditioned to fall entirely into a subpopulation with most recent
common ancestor (MRCA) shorter than $\varepsilon$. First, using the comb
representation of the total genealogy (Lambert & Uribe Bravo 2016), we show
that the genealogy of the descendance of the MRCA of the sample on the
timescale $\varepsilon$ converges as $\varepsilon\to 0$. The limit is the
so-called Brownian coalescent point process (CPP) stopped at an independent
Gamma random variable with parameter $n$, which can be seen as the genealogy at
a large time of the total population of a rescaled critical birth-death
process, biased by the $n$-th power of its size. Secondly, we show that in this
limit the coalescence times of the $n$ sampled individuals are i.i.d. uniform
random variables in $(0,1)$. These results provide a coupling between two
standard models for the genealogy of a random exchangeable population: the
Kingman coalescent and the Brownian CPP.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol