Weak convergence results for the Kakutani interval splitting procedure.

DOI10.1214/aop/1078415840zbMath1049.60025OpenAlexW4251601645MaRDI QIDQ1879858

Ronald Pyke, Willem R. Van Zwet

Publication date: 15 September 2004

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

Full work available at URL: https://doi.org/10.1214/aop/1078415840

zbMATH Keywords

weak convergencecumulantsself-similarityempirical processesspacingsKakutani interval splitting

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Stochastic processes (60G99) Functional limit theorems; invariance principles (60F17)

Related Items (10)

What is Known About Robbins' Problem? ⋮ Discrepancy of \(LS\)-sequences of partitions and points ⋮ The power of online thinning in reducing discrepancy ⋮ Statistics and gap distributions in random Kakutani partitions and multiscale substitution tilings ⋮ An evening spent with Bill van Zwet ⋮ Division point measures resulting from triangle subdivisions ⋮ Benford's law and continuous dependent random variables ⋮ A von Neumann theorem for uniformly distributed sequences of partitions ⋮ Discrepancy of stratified samples from partitions of the unit cube ⋮ Willem van Zwet's research

Cites Work

• Splitting intervals. II: Limit laws for lengths
• Random sequential bisection and its associated binary tree
• The asymptotic behavior of spacings under Kakutani's model for interval subdivision
• A proof of Kakutani's conjecture on random subdivision of longest intervals
• The Stochastic Convergence of a Function of Sample Successive Differences
• A unified model for Kakutani's interval splitting and Rényi's random packing
• Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems
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