Increasing paths on N-ary trees

Abstract : 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2014
Domaine :

https://hal.archives-ouvertes.fr/hal-00955505
Contributeur : Xinxin Chen <>
Soumis le : mardi 4 mars 2014 - 15:44:15
Dernière modification le : lundi 29 mai 2017 - 14:23:55
Document(s) archivé(s) le : mercredi 4 juin 2014 - 11:47:08

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Increasing_paths_on_trees.pdf
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• HAL Id : hal-00955505, version 1
• ARXIV : 1403.0843

Citation

Xinxin Chen. Increasing paths on N-ary trees. 2014. <hal-00955505>

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