Binary trees, exploration processes, and an extented Ray--Knight Theorem

Abstract

We study the bijection between binary Galton--Watson trees in continuous time and their exploration process, both in the sub- and in the supercritical cases. We then take the limit over renormalized quantities, as the size of the population tends to infinity. We thus deduce Delmas' generalization of the second Ray--Knight theorem.

References in corpus (2)

• Growth of the Brownian forest
• Height process for super-critical continuous state branching process

Cited by in corpus (4)

• Trees under attack: a Ray-Knight representation of Feller's branching diffusion with logistic growth
• Time reversal dualities for some random forests
• The height process of a continuous state branching process with interaction
• A note on the scaling limits of contour functions of Galton-Watson trees