2026/07/20 by Shirshendu Ganguly, Victor Ginsburg, Zoe Himwich
#math.PR #math-ph #math.MP
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 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 (β1, β2), and shows that they decouple in the limit β2 ≫ β1 ≫ 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].