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KPZ fixed point convergence of the ASEP and stochastic six-vertex models

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arxiv 2412.18117 v1 pith:CLFMRG6V submitted 2024-12-24 math.PR math-phmath.MP

KPZ fixed point convergence of the ASEP and stochastic six-vertex models

classification math.PR math-phmath.MP
keywords asepfixedmodelspointsix-vertexstochasticunderapproach
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that the height functions of these models converge to the KPZ fixed point. Previously, our results were known in the case of ASEP (for a particular direction in the rarefaction fan) via a comparison approach arXiv:2008.06584.

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Cited by 5 Pith papers

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

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    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.

  2. Shocks, instability, and the twenty networks of infinite geodesics in the Directed Landscape

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  4. Two-time spatial decorrelation for the flat KPZ fixed point

    math.PR 2026-07 conditional novelty 6.0

    The two-time spatial covariance of the flat KPZ fixed point decays as exp(-c|x|^3), and normalized spatial averages converge to a Gaussian process with covariance equal to the space-integrated two-time correlation.

  5. The censored stochastic six-vertex model and parabolic Kazhdan--Lusztig $R$-polynomials

    math.PR 2026-06 unverdicted novelty 6.0

    Introduces censored stochastic six-vertex model and proves stochastic domination plus intertwining relation via parabolic Kazhdan-Lusztig R-polynomials.