General Edgeworth expansions with applications to profiles of random trees

DOI10.1214/17-AAP1285zbMath1382.60068arXiv1606.03920MaRDI QIDQ1704141

Zakhar Kabluchko, Alexander Marynych, Henning Sulzbach

Publication date: 8 March 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.03920

zbMATH Keywords

profilewidthcentral limit theoremEdgeworth expansionbranching random walkmoderandom treerandom analytic functionbiggins martingalemod-phi convergence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Applications of branching processes (60J85) Large deviations (60F10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (11)

Limit theorems for supercritical branching processes in random environment ⋮ Tree evolution processes for bucket increasing trees ⋮ Random cones in high dimensions II: Weyl cones ⋮ Mod-\( \phi\) convergence of Stirling distributions and limit theorems for zeros of their generating functions ⋮ \(r\)-Lah distribution: properties, limit theorems and an application to compressed sensing ⋮ Weak convergence of the number of vertices at intermediate levels of random recursive trees ⋮ Random walks with preferential relocations and fading memory: a study through random recursive trees ⋮ A functional limit theorem for the profile of random recursive trees ⋮ Self-similar solutions of kinetic-type equations: the boundary case ⋮ Geometry of weighted recursive and affine preferential attachment trees ⋮ Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks

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