Stochastic six-vertex model in a half-quadrant and half-line open ASEP

Abstract

We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin fluctuates asymptotically (in large time $\tau$) according to the Tracy-Widom GOE distribution on the ${\tau }^{1/3}$ scale. This is the first example of KPZ asymptotics for a half-space system outside the class of free-fermionic/determinantal/Pfaffian models. Our main tool in this analysis is a new class of probability measures on Young diagrams that we call half-space Macdonald processes, as well as two surprising relations. The first relates a special (Hall-Littlewood) case of these measures to the half-space stochastic six-vertex model (which further limits to ASEP) using a Yang-Baxter graphical argument. The second relates certain averages under these measures to their half-space (or Pfaffian) Schur process analogs via a refined Littlewood identity.

49 pages. v3: minor typos corrected. v2: added references and improved introduction

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Cited by in corpus (33)

• The KPZ Limit of ASEP with Boundary
• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Lower tail of the KPZ equation
• Pfaffian Schur processes and last passage percolation in a half-quadrant
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• The free boundary Schur process and applications I
• Half-space Macdonald processes
• Half-space stationary Kardar-Parisi-Zhang equation
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line
• Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media
• Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
• Stationary half-space last passage percolation
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line: the height statistics at a shifted point
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model
• The lower tail of the half-space KPZ equation
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• Lyapunov exponents of the half-line SHE
• Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian case
• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
• Boundary matrices for the higher spin six vertex model
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• Approximating the stationary distribution of the ASEP with open boundaries
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• Stochastic symplectic ice
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• Tracy-Widom asymptotics for a river delta model
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• Stationary measure for six-vertex model on a strip
• Height distributions in interface growth: The role of the averaging process
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$
• The second class particle in the half-line open TASEP
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution