Rigorous results for the NK model
Publication
, Journal Article
Durrett, R; Limic, V
Published in: Annals of Probability
October 1, 2003
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.
Duke Scholars
Published In
Annals of Probability
DOI
ISSN
0091-1798
Publication Date
October 1, 2003
Volume
31
Issue
4
Start / End Page
1713 / 1753
Related Subject Headings
- Statistics & Probability
- 0104 Statistics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Durrett, R., & Limic, V. (2003). Rigorous results for the NK model. Annals of Probability, 31(4), 1713–1753. https://doi.org/10.1214/aop/1068646364
Durrett, R., and V. Limic. “Rigorous results for the NK model.” Annals of Probability 31, no. 4 (October 1, 2003): 1713–53. https://doi.org/10.1214/aop/1068646364.
Durrett R, Limic V. Rigorous results for the NK model. Annals of Probability. 2003 Oct 1;31(4):1713–53.
Durrett, R., and V. Limic. “Rigorous results for the NK model.” Annals of Probability, vol. 31, no. 4, Oct. 2003, pp. 1713–53. Scopus, doi:10.1214/aop/1068646364.
Durrett R, Limic V. Rigorous results for the NK model. Annals of Probability. 2003 Oct 1;31(4):1713–1753.
Published In
Annals of Probability
DOI
ISSN
0091-1798
Publication Date
October 1, 2003
Volume
31
Issue
4
Start / End Page
1713 / 1753
Related Subject Headings
- Statistics & Probability
- 0104 Statistics
- 0101 Pure Mathematics