LINEAR-OPERATORS ON CORRELATED LANDSCAPES

In this contribution we consider the effect of a class of ''averaging operators'' on isotropic fitness landscapes. Explicit expressions for the correlation function of the averaged landscapes are derived. A new class of tunably rugged landscapes, obtained by iterated smoothing of the random energy model, is established. The correlation structure of certain landscapes, among them the Sherrington-Kirkpatrick model, remains unchanged under the action of all averaging operators considered here.