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arXiv · 2404.16801

The directed landscape is a black noise

Zoe Himwich·Shalin Parekh
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Abstract

We show that the directed landscape is a black noise in the sense of Tsirelson and Vershik. As a corollary, we show that for any microscopic system in which the height profile converges in law to the directed landscape, the driving noise is asymptotically independent of the height profile. This decoupling result provides one answer to the question of what happens to the driving noise in the limit under the KPZ scaling, and illustrates a type of noise sensitivity for systems in the KPZ universality class. Such decoupling and sensitivity phenomena are not present in the intermediate-disorder or weak-asymmetry regime, thus illustrating a contrast from the weak KPZ scaling regime. Along the way, we prove a strong mixing property for the directed landscape on a bounded time interval under spatial shifts, with a mixing rate $α(N)\leq Ce^{-dN^3}$ for some $C,d>0$.

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Zoe Himwich, Shalin Parekh. 2025-04-07. The directed landscape is a black noise. https://arxiv.org/abs/2404.16801

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