Published November 1991
| Published
Journal Article
Open
A Large Deviation Rate and Central Limit Theorem for Horton Ratios
- Creators
- Wang, Stanley Xi
- Waymire, Edward C.
Abstract
Although originating in hydrology, the classical Horton analysis is based on a geometric progression that is widely used in the empirical analysis of branching patterns found in biology, atmospheric science, plant pathology, etc., and more recently in tree register allocation in computer science. The main results of this paper are a large deviation rate and a central limit theorem for Horton bifurcation ratios in a standard network model. The methods are largely self-contained. In particular, derivations of some previously known results of the theory are indicated along the way.
Additional Information
© 1991 Society for Industrial and Applied Mathematics. Received by the editors April 24, 1989; accepted for publication (in revised form) November 16, 1990. This author was partially supported as a Graduate Research Assistant under grant 26220-GS from the Army Research Office. This research was supported in part by grant 26220-GS from the Army Research Office and the Mathematical Sciences Institute of Cornell University and National Science Foundation grant DMS-8801466. We learned about the connections with classical combinatorial identities and the first method of proof of Lemma 2.1 from Otto G. Ruehr. We also thank Rabi Bhattacharya for some helpful discussions.Attached Files
Published - WANsiamjdm91.pdf
Files
WANsiamjdm91.pdf
Files
(1.2 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:a01a277ffda27de06c4888c37d5f5449
|
1.2 MB | Preview Download |
Additional details
- Eprint ID
- 30282
- Resolver ID
- CaltechAUTHORS:20120424-110658782
- 26220-GS
- Army Research Office (ARO)
- Cornell University Mathematical Sciences Institute
- DMS-8801466
- NSF
- Created
-
2012-04-24Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field