Wang, Stanley Xi and Waymire, Edward C. (1991) A Large Deviation Rate and Central Limit Theorem for Horton Ratios. SIAM Journal on Discrete Mathematics, 4 (4). pp. 575-588. ISSN 0895-4801 http://resolver.caltech.edu/CaltechAUTHORS:20120424-110658782
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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.
| Item Type: | Article | ||||||||
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| 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. | ||||||||
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| Subject Keywords: | random tree; bifurcation ratio; large deviation; central limit theorem | ||||||||
| Classification Code: | AMS Subject Headings: primary 60F10, 60F05, 60C05; secondary 86A05, 60J85 | ||||||||
| Record Number: | CaltechAUTHORS:20120424-110658782 | ||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20120424-110658782 | ||||||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 30282 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | Jason Perez | ||||||||
| Deposited On: | 24 Apr 2012 18:35 | ||||||||
| Last Modified: | 26 Dec 2012 15:06 |
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