On the asymptotic behaviour of random recursive trees in random environments

DOI10.1239/aap/1165414591zbMath1107.05082arXivmath/0608211OpenAlexW4238472355MaRDI QIDQ3419856

Vladimir A. Vatutin, Konstantin A. Borovkov

Publication date: 31 January 2007

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608211

zbMATH Keywords

random environmentrandom recursive treeoutdegreeSpitzer's conditiondistance to the root

Mathematics Subject Classification ID

Trees (05C05) Random graphs (graph-theoretic aspects) (05C80) Sums of independent random variables; random walks (60G50) Limit theorems in probability theory (60F99)

Related Items (11)

Condensation phenomena in preferential attachment trees with neighbourhood influence ⋮ On the Asymptotic Behavior of a Dynamic Version of the Neyman Contagious Point Process ⋮ Tree evolution processes for bucket increasing trees ⋮ Random gluing of metric spaces ⋮ Degree distributions in recursive trees with fitnesses ⋮ Fine asymptotics for the maximum degree in weighted recursive trees with bounded random weights ⋮ Random walks with preferential relocations and fading memory: a study through random recursive trees ⋮ The \(k\)-cut model in deterministic and random trees ⋮ Geometry of weighted recursive and affine preferential attachment trees ⋮ Dynamical models for random simplicial complexes ⋮ Correction terms for the height of weighted recursive trees

Cites Work

• Applications of the theory of records in the study of random trees
• The random difference equation \(X_ n = A_ n X_{n-1} + B_ n\) in the critical case
• A note on the growth of random trees
• Criticality for branching processes in random environment
• On the asymptotic behaviour of a simple growing point process model
• Spitzer's condition and ladder variables in random walks
• On conditioning a random walk to stay nonnegative
• The degree sequence of a scale-free random graph process
• Emergence of Scaling in Random Networks
• Note on the heights of random recursive trees and random m‐ary search trees
• Comportement asymptotique du noyau potentiel sur les groupes de Lie
• Probability metrics and recursive algorithms
• Galton--Watson Branching Processes in a Random Environment. II: Finite-dimensional Distributions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the asymptotic behaviour of random recursive trees in random environments