Emmanuel Schertzer, LPMA-UPMC

The scaling limit of CMJ forests.

Crump-Mode-Jagers (CMJ) trees generalize Galton-Watson trees by allowing individuals to live for an arbitrary duration and give birth at arbitrary times during their life-time. In this talk, I will focus on the height and contour processes encoding a general CMJ forest. I will first show that the height process can be expressed in terms of a random transformation of the ladder height process associated with the underlying Lukasiewicz path. I will present two applications of this result: (1) in the case of ``short'' edges, the height process of a CMJ is obtained by stretching by a constant factor the height process of the associated genealogical Galton-Watson tree, and (2) when the offspring distribution has a finite second moment, the genealogy of the CMJ can be obtained from the underlying genealogical structure by a marking procedure, related to the so-called Poisson snake.