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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.
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https://hal.archives-ouvertes.fr/hal-00955505
Contributor : Xinxin Chen <>
Submitted on : Tuesday, March 4, 2014 - 3:44:15 PM
Last modification on : Saturday, March 28, 2020 - 2:16:36 AM
Document(s) archivé(s) le : Wednesday, June 4, 2014 - 11:47:08 AM

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

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

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