Asymptotic expansions and precise deviations in the Kingman coalescent

Abstract

In this paper, we study the small-time asymptotic behavior of the Kingman coalescent. We obtain the Berry-Esseen bound and the Edgeworth expansion in the central limit theorem. Moreover, by the method of mod-ϕ convergence, we also obtain the precise large deviations and the precise moderate deviations. Last, we also obtain a non-asymptotic deviation inequality for the Kingman coalescent.