Abstract

We study the tail exponents for the height function of the stationary stochastic six-vertex model in the moderate deviations regime. For the upper tail of the height function we find upper and lower bounds of matching order, with a tail exponent of $\frac{3}{2}$, characteristic of KPZ distributions. We also obtain an upper bound for the lower tail of the same order.

Our results for the stochastic six-vertex model hold under a restriction on the model parameters for which a certain “microscopic concavity” condition holds. Nevertheless, our estimates are sufficiently strong to pass through the degeneration of the stochastic six-vertex model to the ASEP. We therefore obtain tail estimates for both the current as well as the location of a second-class particle in the ASEP with stationary (Bernoulli) initial data. Our estimates complement the variance bounds obtained in the seminal work of Balázs and Seppäläinen.

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