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.
Publié le : 2003-10-14
Classification:
NK model,
fitness,
local maxima,
limit theorems,
R-recurrence,
60G50,
60F05
@article{1068646364,
author = {Durrett, Richard and Limic, Vlada},
title = {Rigorous results for the N K model},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 1713-1753},
language = {en},
url = {http://dml.mathdoc.fr/item/1068646364}
}
Durrett, Richard; Limic, Vlada. Rigorous results for the N K model. Ann. Probab., Tome 31 (2003) no. 1, pp. 1713-1753. http://gdmltest.u-ga.fr/item/1068646364/