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KPZ fixed point convergence of the ASEP and stochastic six-vertex models
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abstract
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.
Forward citations
Cited by 3 Pith papers
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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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Invariant measures and shocks in the KPZ fixed point
Every extremal invariant measure of the recentered KPZ fixed point is a Brownian motion with drift, and new shock-frame measures of Brownian plus Bessel form are constructed and shown to arise from open-boundary stati...
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Two-time spatial decorrelation for the flat KPZ fixed point
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.
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