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The directed landscape is a black noise
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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 $C,d>0$.
Forward citations
Cited by 5 Pith papers
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Temperature chaos in directed polymers
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.
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Periodic directed landscape
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.
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Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow
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.
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Stochastic heat flow is a black noise
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.
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The Critical 2d Stochastic Heat Flow and Related Models
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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