Estimating some features of \(NK\) fitness landscapes.
The authors reduce some asymptotic features of \(NK\) fitness landscapes to questions about eigenvalues and Lyapunov exponents. When \(K\) is fixed, the expected number of local maxima grows exponentially with \(N\) at a rate depending on the top eigenvalue of a kernel derived from the distribution of the fitness, and the average height of a local maximum converges to a value determined by the corresponding eigenfunction. The global maximum converges in probability as \(N\rightarrow\infty\) to a constant given by the top Lyapunov exponent for a system of i.i.d. max-plus random matrices, and this constant is nondecreasing with \(K\). Various such quantities are computed for certain special cases when \(K\) is small, and these calculations can, in principle, be extended to larger \(K\).
scientific article; zbMATH DE number 1906151