The Beta(p,1) extensions of the random (uniform) Cantor sets
Discussiones Mathematicae. Probability and Statistics, Tome 29 (2009) no. 2, pp. 199-221
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Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing defined by the appropriate Beta(p,1) order statistics. We investigate the reasons why the Hausdorff dimension of this deterministic fractal is greater than the Hausdorff dimension of the corresponding random fractals.
Keywords:
order statistics, uniform spacings, random middle third Cantor set, Beta spacings, Hausdorff dimension
@article{DMPS_2009_29_2_a6,
author = {Pestana, Dinis and Aleixo, Sandra and Leonel Rocha, J.},
title = {The {Beta(p,1)} extensions of the random (uniform) {Cantor} sets},
journal = {Discussiones Mathematicae. Probability and Statistics},
pages = {199--221},
publisher = {mathdoc},
volume = {29},
number = {2},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMPS_2009_29_2_a6/}
}
TY - JOUR AU - Pestana, Dinis AU - Aleixo, Sandra AU - Leonel Rocha, J. TI - The Beta(p,1) extensions of the random (uniform) Cantor sets JO - Discussiones Mathematicae. Probability and Statistics PY - 2009 SP - 199 EP - 221 VL - 29 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMPS_2009_29_2_a6/ LA - en ID - DMPS_2009_29_2_a6 ER -
%0 Journal Article %A Pestana, Dinis %A Aleixo, Sandra %A Leonel Rocha, J. %T The Beta(p,1) extensions of the random (uniform) Cantor sets %J Discussiones Mathematicae. Probability and Statistics %D 2009 %P 199-221 %V 29 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMPS_2009_29_2_a6/ %G en %F DMPS_2009_29_2_a6
Pestana, Dinis; Aleixo, Sandra; Leonel Rocha, J. The Beta(p,1) extensions of the random (uniform) Cantor sets. Discussiones Mathematicae. Probability and Statistics, Tome 29 (2009) no. 2, pp. 199-221. http://geodesic.mathdoc.fr/item/DMPS_2009_29_2_a6/