Ruelle - Perron - Frobenius Operator Approach to the Annealed Pinning Model with Gaussian Long-Range Correlated Disorder

#### J. Poisat

2013, v.19, №3, 577-606

ABSTRACT

In this paper we study the pinning model with correlated Gaussian disorder. The presence of correlations makes the annealed model more involved than the usual homogeneous model, which is fully solvable. We prove however that if the disorder correlations decay fast enough then the annealed critical behaviour is the same as the homogeneous one. Our result is sharper if the decay is exponential. The approach we propose relies on the spectral properties of a transfer or Ruelle - Perron - Frobenius operator related to the model. We use results on these operators that were obtained in the framework of the thermodynamic formalism for countable Markov shifts. We also provide large-temperature asymptotics of the annealed critical curve under weaker assumptions.

Keywords: pinning model,correlated disorder,free energy,annealed,critical exponent,Harris criterion,Ruelle - Perron - Frobenius operator,countable Markov shifts,phase transition,subadditivity