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Three mechanisms for power laws on the Cayley tree

Brookings, Ted and Carlson, J. M. and Doyle, John (2005) Three mechanisms for power laws on the Cayley tree. Physical Review E, 72 (5). Art. no. 056120. ISSN 1539-3755. http://resolver.caltech.edu/CaltechAUTHORS:BROpre05

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Abstract

We compare preferential growth, critical phase transitions, and highly optimized tolerance (HOT) as mechanisms for generating power laws in the familiar and analytically tractable context of lattice percolation and forest fire models on the Cayley tree. All three mechanisms have been widely discussed in the context of complexity in natural and technological systems. This parallel study enables direct comparison of the mechanisms and associated lattice solutions. Criticality fits most naturally into the category of random processes, where power laws are a consequence of fluctuations in an ensemble with no intrinsic scale. The power laws in preferential growth can be understood in the context of competing exponential growth and decay processes. HOT generalizes this functional mechanism involving exponentials of exponentials to a broader class of nonexponential functions, which arise from optimization.


Item Type:Article
Additional Information:©2005 The American Physical Society (Received 5 August 2005; published 16 November 2005) This work was supported by the David and Lucile Packard Foundation, NSF Grant No. DMR-9813752, the James S. McDonnell Foundation, and the Institute for Collaborative Biotechnologies through Grant No. DAAD19-03-D-0004 from the U.S. Army Research Office.
Subject Keywords:random processes; fluctuations; phase transformations; percolation
Record Number:CaltechAUTHORS:BROpre05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BROpre05
Alternative URL:http://dx.doi.org/10.1103/PhysRevE.72.056120
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1516
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:26 Jan 2006
Last Modified:26 Dec 2012 08:44

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