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Abstract

The Statistical Mechanics of Stretched Polymers D. Ioffe, Y. Velenik Braz. J. Probab. Stat. 24 (2), 279-299 (2010). We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our results are stable under suitable small perturbations of these pure cases. We provide in particular a precise description of the stretched phase (local limit theorems for the end-point and local observables, invariance principle, microscopic structure). Our results also characterize precisely the (non-trivial, direction-dependent) critical force needed to trigger the collapsed/stretched phase transition in the attractive case. We also describe some recent progress: first, the determination of the order of the phase transition in the attractive case; second, a proof that a semi-directed polymer in quenched random environment is diffusive in dimensions 4 and higher when the temperature is high enough. In addition, we correct an incomplete argument from an earlier paper. Key words: Self-interacting polymer, phase transition, coarse-graining, Ornstein-Zernike theory, Invariance principle, Quenched disorder Files: PDF file, Published version, bibtex