@inproceedings{170b78efaa65441cba275a40beb17b48,
title = "Refined asymptotics for the number of leaves of random point quadtrees",
abstract = "In the early 2000s, several phase change results from distributional convergence to distributional non-convergence have been obtained for shape parameters of random discrete structures. Recently, for those random structures which admit a natural martingale process, these results have been considerably improved by obtaining refined asymptotics for the limit behavior. In this work, we propose a new approach which is also applicable to random discrete structures which do not admit a natural martingale process. As an example, we obtain refined asymptotics for the number of leaves in random point quadtrees. More applications, for example to shape parameters in generalized m-ary search trees and random gridtrees, will be discussed in the journal version of this extended abstract.",
keywords = "Central limit theorem, Contraction method, Number of leaves, Phase change, Positivity of variance, Quadtree, Stochastic fixed-point equation",
author = "Michael Fuchs and M{\"u}ller, {Noela S.} and Henning Sulzbach",
year = "2018",
month = jun,
day = "25",
doi = "10.4230/LIPIcs.AofA.2018.23",
language = "English",
series = "Leibniz International Proceedings in Informatics (LIPIcs)",
publisher = "Schloss Dagstuhl",
editor = "{Allen Fill}, {James } and {Daniel Ward}, {Mark }",
booktitle = "29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2018",
address = "Germany",
note = "29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2018 ; Conference date: 25-06-2018 Through 29-06-2018",
}