On quenched and annealed critical curves of random pinning model with finite range correlations

Julien Poisat (1)

1 ICJ - Institut Camille Jordan

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.

Mots clés: Polymer models; Pinning; Annealed model; Disorder irrelevance; Correlated disorder; Renewal process; Markov renewal process; Intersection of renewal processes; Perron-Frobenius theory; subadditivity

Domaines: Probabilités [math.PR]

Julien Poisat. On quenched and annealed critical curves of random pinning model with finite range correlations. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2013, 49 (2), pp.456-482. ⟨10.1214/11-AIHP446⟩. ⟨hal-00368656v3⟩