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 [3], showing that a transition occurs when TN ≈ 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 ≈ N1/3 and when TN ≈ √ N respectively. © 2009 Applied Probability Trust.
Caravenna, F., Petrelis, N. (2009). Depinning of a polymer in a multi-interface medium. ELECTRONIC JOURNAL OF PROBABILITY, 14, 2038-2067.
Depinning of a polymer in a multi-interface medium
CARAVENNA, FRANCESCO;
2009
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 [3], showing that a transition occurs when TN ≈ 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 ≈ N1/3 and when TN ≈ √ N respectively. © 2009 Applied Probability Trust.
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