Pinning of a polymer on a disordered line with finite range correlations: the annealed critical curve

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.

Mots clés: polymer models; pinning; annealed model; correlated disorder; renewal process; Perron-Frobenius theory; subadditivity.; subadditivity

Domaines: Probabilités [math.PR]

Julien Poisat. Pinning of a polymer on a disordered line with finite range correlations: the annealed critical curve. 2009. ⟨hal-00368656v2⟩