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On the Contraction Method with Reduced Independence Assumptions

Authors Ralph Neininger, Jasmin Straub

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Author Details

Ralph Neininger
  • Institute for Mathematics, Goethe University, 60054 Frankfurt a.M., Germany
Jasmin Straub
  • Institute for Mathematics, Goethe University, 60054 Frankfurt a.M., Germany

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Ralph Neininger and Jasmin Straub. On the Contraction Method with Reduced Independence Assumptions. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.AofA.2022.14

Abstract

Recursive sequences of laws of random variables (and random vectors) are considered where an independence assumption which is usually made within the setting of the contraction method is dropped. This restricts the study to sequences which after normalization lead to asymptotic normality. We provide a general univariate central limit theorem which can directly be applied to problems from the analysis of algorithms and random recursive structures without further knowledge of the contraction method. Also multivariate central limit theorems are shown and bounds on rates of convergence are provided. Examples include some previously shown central limit analogues as well as new applications on Fibonacci matchings.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
  • Theory of computation → Divide and conquer
Keywords
  • Probabilistic Analysis of Algorithms
  • random Trees
  • weak Convergence
  • Probability Metrics
  • Contraction Method

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