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In this paper we study the pinning model with correlated Gaussian disorder.The presence of correlations makes the annealed model more involved than theusual homogeneous model, which is fully solvable. We prove however that if thedisorder correlations decay fast enough then the annealed critical behaviour isthe same as the homogeneous one. Our result is sharper if the decay isexponential. The approach we propose relies on the spectral properties of atransfer or Ruelle-Perron Frobenius operator related to the model. We useresults on these operators that were obtained in the framework of thethermodynamic formalism for countable Markov shifts. We also providelarge-temperature asymptotics of the annealed critical curve under weakerassumptions.

Ruelle-Perron-Frobenius operator approach to the annealed pinning model with Gaussian long-range correlated disorder