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

Mamadou Ba , Etienne Pardoux (1) , Ahmadou Bamba Sow

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Domaines: Mathématiques [math]; Probabilités [math.PR]

Mamadou Ba, Etienne Pardoux, Ahmadou Bamba Sow. Binary trees, exploration processes, and an extented Ray--Knight Theorem. Journal of Applied Probability, 2012, 49, pp.210-225. ⟨10.1239/jap/1331216843⟩. ⟨hal-01231985⟩