拉伸高聚物的统计力学
The Statistical Mechanics of Stretched Polymers
摘要：
我们描述了一些最近的结果有关的统计性质的自相互作用的聚合物拉伸的外力。我们主要集中在纯吸引或纯排斥的自相互作用的情况下，但我们的结果是稳定的，在适当的小扰动下，这些纯的情况。我们特别提供了一个精确的描述拉伸阶段（局部极限定理的终点和当地的可观，不变原理，微观结构）。我们的研究结果还精确地描述了（非平凡的，方向相关的）临界力需要触发的崩溃/拉伸相变的吸引力的情况下。我们还描述了一些最近的进展：第一，在吸引力的情况下，相变的顺序的确定;第二，证明了在淬火随机环境中的半定向聚合物是扩散的4维和更高的温度是足够高的。此外，我们纠正了一个不完整的论点，从我们早期的作品之一。
英文摘要：
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 one of our earlier works.
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