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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 70 open journal systems 


Depinning of a polymer in a multi-interface medium

Francesco Caravenna, University of Padova
Nicolas Pétrélis, University of Nantes


Abstract
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 = TN 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 Petrelis (2009), showing that a transition occurs when TN groes like 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 {TN}N, showing that two transitions occur, when TN groes like N1/3 and when TN groes like N1/2 respectively.


Full text: PDF

Pages: 2038-2067

Published on: September 28, 2009
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Electronic Journal of Probability. ISSN: 1083-6489