uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Dimension (In)equalities and Holder Continuous Curves in Fractal Percolation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 26, no 3, 836-854 p.Article in journal (Refereed) Published
Abstract [en]

We relate various concepts of fractal dimension of the limiting set in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in (the "dust"). In two dimensions, we also show that the set consisting of connected components larger than one point is almost surely the union of non-trivial Holder continuous curves, all with the same exponent. Finally, we give a short proof of the fact that in two dimensions, any curve in the limiting set must have Hausdorff dimension strictly larger than 1.

Place, publisher, year, edition, pages
2013. Vol. 26, no 3, 836-854 p.
Keyword [en]
Fractal percolation, Hausdorff dimension, Box counting dimension, Holder continuous curves, Subsequential weak limits
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-206963DOI: 10.1007/s10959-012-0413-8ISI: 000323250500011OAI: oai:DiVA.org:uu-206963DiVA: diva2:646640
Available from: 2013-09-09 Created: 2013-09-09 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

fulltext(636 kB)50 downloads
File information
File name FULLTEXT01.pdfFile size 636 kBChecksum SHA-512
481d406fadd65c317082e1c5e7e0bdb21abdf997a6c198b6228724edb72ca18bf9e11abe4df7cb825b2e60fa68f97461c2f49e460ae850f6a718e01d43ba0799
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Authority records BETA

Broman, Erik I.

Search in DiVA

By author/editor
Broman, Erik I.
By organisation
Department of Mathematics
In the same journal
Journal of theoretical probability
Natural Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 50 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 387 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf