Jean-François Delmas

Asymptotic results on the length of coalescent trees

We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

Pruning Galton–Watson trees and tree-valued Markov processes

We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process

Super-mouvement brownien avec catalyse

\{ {\cal G}(u)\}

Smaller population size at the MRCA time for stationary branching processes

by pruning Galton-Watson trees and an analogous process

Changing the branching mechanism of a continuous state branching process using immigration

\{{\cal G}^*(u)\}

Critical Multi-type Galton–Watson Trees Conditioned to be Large

by pruning a critical or subcritical Galton-Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process

Maximum entropy copula with given diagonal section

\{{\cal G}(u)\}

Asymptotics for the small fragments of the fragmentation at nodes

run until its ascension time has a representation in terms of

Optimal exponential bounds for aggregation of estimators for the Kullback-Leibler loss

\{{\cal G}^*(u)\}

Total length of the genealogical tree for quadratic stationary continuous-state branching processes

. A similar result was obtained by Aldous and Pitman (1998) in the special case of Poisson offspring distributions where they considered uniform pruning of Galton-Watson trees by adding marks on the edges of trees.