Linear operators on correlated landscapes

(Received 26 October 1993, received in final form 12 January 1994, accepted 28 January 1994)

Abstract
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.