Linear Operators on Correlated Landscapes

Peter F. Stadler

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 tuneably 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.

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