Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 13 (2018), 2457-2529.
Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process
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 ) according to the Tracy–Widom Gaussian orthogonal ensemble distribution on the -scale. This is the first example of Kardar–Parisi–Zhang 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 the ASEP) using a Yang–Baxter graphical argument. The second relates certain averages under these measures to their half-space (or Pfaffian) Schur process analogues via a refined Littlewood identity.
Duke Math. J., Volume 167, Number 13 (2018), 2457-2529.
Received: 12 May 2017
Revised: 16 April 2018
First available in Project Euclid: 27 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B23: Exactly solvable models; Bethe ansatz 05E05: Symmetric functions and generalizations 60H15: Stochastic partial differential equations [See also 35R60] 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
Kardar–Parisi–Zhang universality class interacting particle systems asymmetric simple exclusion process six-vertex model integrable probability Macdonald symmetric functions Yang–Baxter equation
Barraquand, Guillaume; Borodin, Alexei; Corwin, Ivan; Wheeler, Michael. Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process. Duke Math. J. 167 (2018), no. 13, 2457--2529. doi:10.1215/00127094-2018-0019. https://projecteuclid.org/euclid.dmj/1535356817