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Abstract: We describe some recent results concerning the statistical properties of aself-interacting polymer stretched by an external force. We concentrate mainlyon the cases of purely attractive or purely repulsive self-interactions, butour results are stable under suitable small perturbations of these pure cases.We provide in particular a precise description of the stretched phase locallimit theorems for the end-point and local observables, invariance principle,microscopic structure. Our results also characterize precisely thenon-trivial, direction-dependent critical force needed to trigger thecollapsed-stretched phase transition in the attractive case. We also describesome recent progress: first, the determination of the order of the phasetransition in the attractive case; second, a proof that a semi-directed polymerin quenched random environment is diffusive in dimensions 4 and higher when thetemperature is high enough. In addition, we correct an incomplete argument fromone of our earlier works.



Author: Dmitry Ioffe, Yvan Velenik

Source: https://arxiv.org/



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