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The directed landscape is a black noise

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arxiv 2404.16801 v3 pith:26FXCHBS submitted 2024-04-25 math.PR

classification math.PR
keywords noisedirectedlandscapeblackdecouplingdrivingheightmixing
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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 $\alpha(N)\leq Ce^{-dN^3}$ for some $C,d>0$.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Temperature chaos in directed polymers

    math.PR 2026-07 conditional novelty 8.0 of 10

    For beta1 = o(beta2) both tending to infinity, coupled CDRP free energies at beta1 and beta2 converge to two independent directed landscapes; as a byproduct, the directed landscape is a two-dimensional black noise.

  2. Periodic directed landscape

    math.PR 2026-07 conditional novelty 8.0 of 10

    The periodic directed landscape is constructed by gluing full-space directed landscapes, and proven to be the universal scaling limit of periodic exponential LPP and of periodic ASEP.

  3. Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow

    math.PR 2025-07 conditional novelty 7.0 of 10

    A general, rate-optimal BKS noise-sensitivity criterion is proven, and it yields the independence of the critical 2D Stochastic Heat Flow from the disorder white noise.

  4. Stochastic heat flow is a black noise

    math.PR 2025-06 accept novelty 7.0 of 10

    The stochastic heat flow is a black noise, meaning its linear random-variable space is trivial, and consequently the critical 2d SHE is asymptotically independent of its mollified driving noise.

  5. The Critical 2d Stochastic Heat Flow and Related Models

    math.PR 2024-12 conditional novelty 2.0 of 10

    Review of the proof that 2d directed polymer and stochastic heat equation partition functions converge, in a critical window, to a unique object called the critical 2d stochastic heat flow.

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