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Poisat, Julien

On quenched and annealed critical curves of random pinning model with finite range correlations. (English. French summary) Zbl 1276.82024

Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 2, 456-482 (2013).
The paper is devoted to directed polymers pinned at a disordered and correlated interface. It is assumed that the disorder sequence is a \(q\)-order moving average. It is established 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. The author is able to produce explicit values of the annealed critical curve for \(q= 1\) and \(q=2\) and a weak disorder asymptotic in the general case. By means of the renewal theory approach of pinning, it is established that the constructed processes from the annealed model are particular Markov renewal processes. It is considered the intersection of two replicas of such process and using the method of second moment, the author proves a result of disorder irrelevance.
Reviewer: Farruh Mukhamedov (Kuantan)

Cited in 3 Documents

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60K37 Processes in random environments
60K05 Renewal theory

Keywords:

polymer models; pinning; annealed model; disorder irrelevance; correlated disorder; renewal process; Markov renewal process; intersection of renewal processes; Perron-Frobenius theory; subadditivity
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\textit{J. Poisat}, Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 2, 456--482 (2013; Zbl 1276.82024)
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