Increasing paths on N-ary trees
type: Dataset
description: 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.
issued: 2026-05-06T03:37:44.163203
language: en
modified: 2026-05-06T03:37:44.163207
contact point: Organization
  fn: CCSD
keyword: house-of-cards
keyword: increasing-path
keyword: infoeu-reposemanticspreprint
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00955505

Increasing paths on N-ary trees
type: Distribution
format: HTML
issued: 2026-05-06T03:37:44.164892
modified: 2026-05-06T03:37:44.152948
access URL: https://hal.science/hal-00955505

test_moissonnage_selune
type: Agent