Large deviation principle for the absorption time of the Beta-coalescent via integral functionals

2025/12/19 by Véchambre, Grégoire
#60B10 #60F10 #60J27 #60J55 #60J74 #60J90 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.17418

Abstract

We study some aspects of the absorption time of the Beta(a,b)-Coalescent starting with n blocks. More precisely, when a>1, the absorption time is known to converge to infinity as n goes to infinity, and we prove that it satisfies a large deviation principle. When a ∈ (0,1), it is known that the coalescent comes down from infinity, and we derive bounds for the convergence in the Kolmogorov distance of the distribution of the absorption time as n goes to infinity. To prove our results we introduce a method, inspired from statistical mechanics, that allows to infer the asymptotic behavior of the Laplace transforms of some integral functionals of the Beta-coalescent as the initial number of blocks n goes to infinity. As a by-product of our proofs we also obtain estimates for the record probabilities of the Beta-coalescent.

Citations

• On the fixation probability of an advantageous allele in a population with skewed offspring distribution
• Pareto genealogies arising from a Poisson branching evolution model with selection
• The Lambda-Fleming-Viot process and a connection with Wright-Fisher diffusion
• A coalescent model for the effect of advantageous mutations on the genealogy of a population

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