Rigorous results for the NK model


Journal Article

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 ≥ 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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Limic, V

Published Date

  • October 1, 2003

Published In

Volume / Issue

  • 31 / 4

Start / End Page

  • 1713 - 1753

International Standard Serial Number (ISSN)

  • 0091-1798

Digital Object Identifier (DOI)

  • 10.1214/aop/1068646364

Citation Source

  • Scopus