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October 2003 Rigorous results for the N K model
Richard Durrett, Vlada Limic
Ann. Probab. 31(4): 1713-1753 (October 2003). DOI: 10.1214/aop/1068646364

Abstract

Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0's and 1's of length N based on the values observed in a sliding window of length $K+1$. When $K\ge 1$, the landscape is quite complicated with many local maxima. Its properties have been extensively investigated by simulation but until our work and the independent investigations of Evans and Steinsaltz little was known rigorously about its properties except in the case $K=N-1$. Here, we prove results about the number of local maxima, their heights and the height of the global maximum. Our main tool is the theory of (substochastic) Harris chains.

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Richard Durrett. Vlada Limic. "Rigorous results for the N K model." Ann. Probab. 31 (4) 1713 - 1753, October 2003. https://doi.org/10.1214/aop/1068646364

Information

Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1049.60037
MathSciNet: MR2016598
Digital Object Identifier: 10.1214/aop/1068646364

Subjects:
Primary: 60F05, 60G50

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • October 2003
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