有向聚合物中的温度混沌
Temperature chaos in directed polymers
浏览论文内容
中文总结 AI 辅助
本文研究连续有向随机聚合物（CDRP）的温度混沌性质，通过考虑在一对逆温度下耦合的CDRP自由能，证明在特定极限下它们解耦收敛到独立定向景观，给出首个“跨温度能量去相关”结果，还证明有向景观是二维黑噪声。
中文摘要 AI 辅助
诸如自旋玻璃和聚合物之类的无序系统具有随机能量景观，有许多对应近基态的宏观分离的能量谷。这种高复杂性使这些系统对外部参数扰动极为敏感，例如相关吉布斯测度的支撑可能会宏观变化，即文献中所称的混沌。本文首次对连续有向随机聚合物（CDRP）的温度混沌性质进行严格研究，它由白噪声驱动，由逆温度β参数化，在零温度极限β→∞时收敛到[Dauvergne - Ortmann - Virág '22]中构建的有向景观。主要结果考虑了在一对逆温度(β1,β2)下通过相同白噪声耦合的CDRP自由能，表明在β2≫β1≫1的极限下它们解耦，收敛到一对独立定向景观，这是首个此类“跨温度能量去相关”结果。关键估计测量了最后通过渗流模型中空间细条的“关键性”或“影响力”。作为副产品，证明策略还表明有向景观是二维黑噪声，此前Virág曾猜想过，这是继临界平面渗流和布朗网络之后的第三个二维黑噪声已知示例。
英文摘要
Disordered systems such as spin glasses and polymers characteristically exhibit random energy landscapes with many macroscopically separated energetic valleys corresponding to near-ground states. This high complexity renders these systems extremely sensitive to perturbations of external parameters. For instance, the support of associated Gibbs measures may change macroscopically under such perturbations, a phenomenon known as chaos in the literature. In experiments, chaotic phenomena are typically studied via temperature perturbations. In this article, we initiate the rigorous study of temperature-chaotic properties of the continuum directed random polymer (CDRP), a canonical model in the KPZ universality class. The CDRP is driven by white noise and is parametrized by inverse temperature $β$, and is known [Wu '26, Das-Zhu '24] to converge in the zero-temperature limit $β\to \infty$ to the directed landscape constructed in [Dauvergne-Ortmann-Virág '22], the putative universal scaling limit of models in the KPZ universality class. The main result of this article considers the CDRP free energies coupled through the same white noise at a pair of inverse temperatures $(β_1, β_2)$, and shows that they decouple in the limit $β_2 \gg β_1 \gg 1$, converging to a pair of independent directed landscapes. This is the first such "energetic de-correlation across temperatures" result. Our key estimate measures the "pivotality" or "influence" of spatially thin strips in models of last passage percolation. As a byproduct, the proof strategy also allows to show that the directed landscape is a two-dimensional black noise (in the sense of [Tsirelson-Vershik '98]), previously conjectured by Virág. This provides the third known example of a two-dimensional black noise after critical planar percolation [Schramm-Smirnov '11] and the Brownian web [Ellis-Feldheim '16].
