The Library
The Hausdorff dimension of a class of random self-similar fractal trees
Tools
Croydon, David A. (2007) The Hausdorff dimension of a class of random self-similar fractal trees. Advances in Applied Probability, Vol.39 (No.3). pp. 708-730. doi:10.1239/aap/1189518635 ISSN 0001-8678.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://www.appliedprobability.org/index.aspx?Group...
Abstract
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical properties of an underlying metric space or the scaling factors being bounded uniformly away from 0. However, using a percolative argument, and taking advantage of the tree-like structure of the sets considered here, it is shown that conditions such as these are not necessary. The scaling factors of the recursively defined structures in consideration form what is known as a multiplicative cascade, and results about the height of this random object are also obtained.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Advances in Applied Probability | ||||
Publisher: | Applied Probability Trust | ||||
ISSN: | 0001-8678 | ||||
Official Date: | September 2007 | ||||
Dates: |
|
||||
Volume: | Vol.39 | ||||
Number: | No.3 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 708-730 | ||||
DOI: | 10.1239/aap/1189518635 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |