96-43 Baladi V.

Correlation spectrum of quenched and annealed equilibrium states for random expanding maps (108K, AMSTeX) Feb 17, 96

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Abstract. We show that the integrated transfer operators for positively weighted i.i.d. smooth expanding systems give rise to annealed equilibrium states for a new variational principle. The unique annealed equilibrium state coincides with the unique annealed Gibbs state. Using work of Ruelle and Fried on generalised Fredholm determinants for transfer operators, we prove that the discrete spectrum of the transfer operators coincides with the correlation spectrum of these invariant measures and with the poles of an annealed zeta function. A modified integrated transfer operator is introduced, which describes the (relativised) quenched states studied e.g. by Kifer. For small random perturbations we obtain stability results on the quenched and annealed measures and spectra by applying perturbative results of Young and the author.

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