ArticleOriginal scientific text
Title
The Beta(p,1) extensions of the random (uniform) Cantor sets
Authors 1, 2, 2
Affiliations
- FCUL, DEIO, CEAUL, Universidade de Lisboa, Campo Grande, Edifício C4, 1749-016 Lisboa, Portugal
- Mathematics Unit, DEC, DEQ, Instituto Superior de Engenharia de Lisboa and CEAUL, Rua Conselheiro Emídio Navarro, 1, 1949-014 Lisboa, Portugal
Abstract
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
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Pages:
199-221
Main language of publication
English
Received
2009-10-06
Published
2009
DOI: 10.7151/dmps.1115
Exact and natural sciences