J. Phys. I France
Volume 4, Numéro 5, May 1994
Page(s) 681 - 696
DOI: 10.1051/jp1:1994170
J. Phys. I France 4 (1994) 681-696

Linear operators on correlated landscapes

Peter F. Stadler

Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, NM 87501, U.S.A.

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

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.

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