The paper claims that for the Kingman coalescent, the probability that the block count equals (2+v√t)/t at small time t is asymptotic to a Gaussian-type expression of order √t.
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Integral representation of probabilities in Kingman coalescent
The paper claims that for the Kingman coalescent, the probability that the block count equals (2+v√t)/t at small time t is asymptotic to a Gaussian-type expression of order √t.