On random split of the segment

Milena Bieniek, and Dominik Szynal. "On random split of the segment." Applicationes Mathematicae 32.3 (2005): 243-261. <http://eudml.org/doc/279542>.

@article{MilenaBieniek2005,
abstract = {We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These actions are repeated indefinitely. We investigate the probability distribution of the lengths of the consecutive pieces after n splits.},
author = {Milena Bieniek, Dominik Szynal},
journal = {Applicationes Mathematicae},
keywords = {random partition; uniform split; splitting in half; random choice; moments; covariance; convergence in probability and almost sure},
language = {eng},
number = {3},
pages = {243-261},
title = {On random split of the segment},
url = {http://eudml.org/doc/279542},
volume = {32},
year = {2005},
}

TY - JOUR
AU - Milena Bieniek
AU - Dominik Szynal
TI - On random split of the segment
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 3
SP - 243
EP - 261
AB - We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These actions are repeated indefinitely. We investigate the probability distribution of the lengths of the consecutive pieces after n splits.
LA - eng
KW - random partition; uniform split; splitting in half; random choice; moments; covariance; convergence in probability and almost sure
UR - http://eudml.org/doc/279542
ER -