zbMATH — the first resource for mathematics

Depinning of a polymer in a multi-interface medium. (English) Zbl 1192.60105
Summary: 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 by F. Caravenna and N. Pétrélis [Ann. Appl. Probab. 19, No. 5, 1803–1839 (2009; Zbl 1206.60089)], showing that a transition occurs when $$T_{N}$$ grows 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 $${T_{N}}_{N}$$, showing that two transitions occur, when $$T_{N}$$ grows like $$N^{1/3}$$ and when $$T_{N}$$ groes like $$N^{1/2}$$ respectively.

MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60F05 Central limit and other weak theorems 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
Full Text: