A functional limit theorem for the profile of random recursive trees

DOI10.1214/18-ECP188zbMath1406.60051arXiv1801.04606MaRDI QIDQ1725478

Zakhar Kabluchko, Aleksander M. Iksanov

Publication date: 14 February 2019

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.04606

zbMATH Keywords

profilefunctional limit theorembranching random walkrandom recursive treeintegrated Brownian motioncrump-mode-jagers branching processlow levels

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Combinatorial probability (60C05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Renewal theory for iterated perturbed random walks on a general branching process tree: Early generations ⋮ Weak convergence of random processes with immigration at random times ⋮ A functional limit theorem for general shot noise processes ⋮ Weak convergence of the number of vertices at intermediate levels of random recursive trees

Cites Work

• Unnamed Item
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• Moment convergence of first-passage times in renewal theory
• Asymptotics of random processes with immigration. I: Scaling limits.
• Martingales and profile of binary search trees
• Profiles of random trees: Limit theorems for random recursive trees and binary search trees
• Branching processes in the analysis of the heights of trees
• On the moments and limit distributions of some first passage times
• General Edgeworth expansions with applications to profiles of random trees
• The profile of binary search trees
• Functional limit theorems for renewal shot noise processes with increasing response functions
• A functional limit theorem for the profile of search trees
• Martingales and large deviations for binary search trees
• Renewal Theory for Perturbed Random Walks and Similar Processes
• Degree distribution in the lower levels of the uniform recursive tree
• Random Trees
• Stopped Random Walks
• An alternative proof of Lorden&s renewal inequality
• Note on the heights of random recursive trees and random m‐ary search trees

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