On quenched and annealed critical curves of random pinning model with finite range correlations Julien Poisat 1Institut Camille Jordan 43 bld du 11 novembre 1918 69622 Villeurbanne, France Tel.: +33(0)472.44.79.41 e-mail: Abstract: This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a q-order moving average and show that the critical curve of the annealed model can be expressed in terms of the Perron-Frobenius eigenvalue of an explicit transfer matrix, which generalizes the annealed bound of the critical curve for i.i.d. disorder. We provide explicit values of the annealed critical curve for q = 1,2 and a weak disorder asymptotic in the general case. Following the renewal theory approach of pinning, the processes arising in the study of the annealed model are particular Markov renewal processes. We consider the intersection of two replicas of this process to prove a result of disorder irrelevance (i.e. quenched and annealed critical curves as well as exponents coincide) via the method of second moment. AMS 2000 subject classifications: 82B44, 60K37, 60K05. Keywords and phrases: Polymer models, Pinning, Annealed model, Dis- order irrelevance, Correlated disorder, Renewal process, Markov renewal process, Intersection of renewal processes, Perron-Frobenius theory, subad- ditivity.
- markov renewal
- dna molecule
- standard gaussian
- contact point
- correlated disorder
- all ?
- annealed model
- independent standard
- random variable