The Annals of Applied Probability

Path properties of the disordered pinning model in the delocalized regime

Kenneth S. Alexander and Nikos Zygouras

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We study the path properties of a random polymer attracted to a defect line by a potential with disorder, and we prove that in the delocalized regime, at any temperature, the number of contacts with the defect line remains in a certain sense “tight in probability” as the polymer length varies. On the other hand we show that at sufficiently low temperature, there exists a.s. a subsequence where the number of contacts grows like the log of the length of the polymer.

Article information

Ann. Appl. Probab., Volume 24, Number 2 (2014), 599-615.

First available in Project Euclid: 10 March 2014

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Zentralblatt MATH identifier

Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 82D60: Polymers 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Depinning transition pinning model path properties


Alexander, Kenneth S.; Zygouras, Nikos. Path properties of the disordered pinning model in the delocalized regime. Ann. Appl. Probab. 24 (2014), no. 2, 599--615. doi:10.1214/13-AAP930.

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