A functional central limit theorem for branching random walks, almost sure weak convergence and applications to random trees

DOI10.1214/16-AAP1188zbMath1367.60028arXiv1410.0469OpenAlexW2964043144MaRDI QIDQ511484

Rudolf Grübel, Zakhar Kabluchko

Publication date: 21 February 2017

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

Full work available at URL: https://arxiv.org/abs/1410.0469

zbMATH Keywords

functional central limit theorembinary search treesstable convergenceGalton-Watson processesrandom recursive treesbranching random walksPólya urnsGaussian analytic functionalmost sure weak convergencemixing convergencequicksort distribution

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Searching and sorting (68P10) Sums of independent random variables; random walks (60G50) Convergence of probability measures (60B10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (7)

Asymptotic expansions in the central limit theorem for a branching Wiener process ⋮ Logarithmic integrals, zeta values, and tiered binomial coefficients ⋮ Edgeworth expansions for profiles of lattice branching random walks ⋮ General Edgeworth expansions with applications to profiles of random trees ⋮ On martingale tail sums for the path length in random trees ⋮ On martingale tail sums in affine two-color urn models with multiple drawings ⋮ On \(L^p\)-convergence of the Biggins martingale with complex parameter

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