Tail estimates for the stationary stochastic six vertex model and ASEP

Abstract

This work studies 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.}

arXiv comment53 pages, 7 figures. v4: minor revisions

References in corpus (19)

• Scaling for a one-dimensional directed polymer with boundary conditions
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Integral Formulas for the Asymmetric Simple Exclusion Process
• Stochastic six-vertex model
• Stochastic higher spin vertex models on the line
• Second class particles and cube root asymptotics for Hammersley's process
• Current Fluctuations of the Stationary ASEP and Six-Vertex Model
• Lower tail of the KPZ equation
• Microscopic concavity and fluctuation bounds in a class of deposition processes
• Formulas for ASEP with Two-Sided Bernoulli Initial Condition
• Fluctuations of the log-gamma polymer free energy with general parameters and slopes
• Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• Upper tail bounds for stationary KPZ models
• Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble
• Pearcey universality at cusps of polygonal lozenge tiling
• Coarsening model on ${\mathbb{Z}}^d$ with biased zero-energy flips and an exponential large deviation bound for ASEP
• Short- and long-time path tightness of the continuum directed random polymer
• Large deviations for the $q$-deformed polynuclear growth

Cited by in corpus (1)

• The stochastic six-vertex model speed process