arXiv subjects

Airam Blancas Benítez

Publications and source records attributed to Airam Blancas Benítez.

2 recordsLinked to original sources

arXiv2018

The Nested Kingman Coalescent: Speed of Coming Down from Infinity

The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends from infinity in this hierarchical coalescent process and prove the existence of an early-time phase during which the number of lineages at time $t$ decays as $ 2γ/ct^2$, where $c$ is the ratio of the coalescence rates at the individual and species levels, and the constant $γ\approx 3.45$ is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time.

math.PR↗

arXiv2015

On branching process with rare neutral mutation

In this paper we study the genealogical structure of a Galton-Watson process with neutral mutations, where the initial population is large and mutation rate is small \cite{B2}. Namely, we extend in two directions the results obtained in Bertoin's work. In the critical case, we construct the version of Bertoin's model conditioned not to be extinct, and in the case with finite variance we show convergence after normalization, of allelic sub-populations towards a tree indexed CSBP with immigration. Besides, we establish the version of the limit theorems in \cite{B2}, been for the unconditioned process and for the process conditioned to non-extinction, in the case where the reproduction law has infinite variance and it is in the domain of attraction of an $α$-stable distribution.

math.PR↗