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15 September 2018 Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process
Guillaume Barraquand, Alexei Borodin, Ivan Corwin, Michael Wheeler
Duke Math. J. 167(13): 2457-2529 (15 September 2018). DOI: 10.1215/00127094-2018-0019


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 τ) according to the Tracy–Widom Gaussian orthogonal ensemble distribution on the τ1/3-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.


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Guillaume Barraquand. Alexei Borodin. Ivan Corwin. Michael Wheeler. "Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process." Duke Math. J. 167 (13) 2457 - 2529, 15 September 2018.


Received: 12 May 2017; Revised: 16 April 2018; Published: 15 September 2018
First available in Project Euclid: 27 August 2018

zbMATH: 06970973
MathSciNet: MR3855355
Digital Object Identifier: 10.1215/00127094-2018-0019

Primary: 60K35
Secondary: 05E05 , 60H15 , 82B23 , 82D30

Keywords: Asymmetric simple exclusion process , integrable probability , interacting particle systems , Kardar–Parisi–Zhang universality class , Macdonald symmetric functions , Six-vertex model , Yang–Baxter equation

Rights: Copyright © 2018 Duke University Press


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Vol.167 • No. 13 • 15 September 2018
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