Open Access
2009 Depinning of a polymer in a multi-interface medium
Francesco Caravenna, Nicolas Pétrélis
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Electron. J. Probab. 14: 2038-2067 (2009). DOI: 10.1214/EJP.v14-698


In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by $T = T_N$ and is allowed to grow with the size $N$ of the polymer. When the polymer receives a positive reward for touching the interfaces, its asymptotic behavior has been derived in Caravenna and Petrelis (2009), showing that a transition occurs when $T_N \approx \log N$. In the present paper, we deal with the so-called depinning case, i.e., the polymer is repelled rather than attracted by the interfaces. Using techniques from renewal theory, we determine the scaling behavior of the model for large $N$ as a function of $\{T_N\}_{N}$, showing that two transitions occur, when $T_N \approx N^{1/3}$ and when $T_N \approx \sqrt{N}$ respectively.


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Francesco Caravenna. Nicolas Pétrélis. "Depinning of a polymer in a multi-interface medium." Electron. J. Probab. 14 2038 - 2067, 2009.


Accepted: 28 September 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1192.60105
MathSciNet: MR2550292
Digital Object Identifier: 10.1214/EJP.v14-698

Primary: 60K35
Secondary: 60F05 , 82B41

Keywords: Localization/delocalization transition , pinning model , Polymer model , Random walk , renewal theory

Vol.14 • 2009
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