Increasing paths on N-ary trees

Xinxin Chen (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Consider a rooted $N$-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible vertices and kill all the others. For any positive constant $\alpha$, we describe the asymptotic behaviors of the population at the $\alpha N$-th generation as $N$ goes to infinity. We also study the criticality of the survival probability at the $(eN-\frac{3}{2}\log N)$-th generation in this paper.

Mots clés: Increasing path; House of Cards.; House of Cards

Domaines: Probabilités [math.PR]

Xinxin Chen. Increasing paths on N-ary trees. 2014. ⟨hal-00955505⟩