Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process
Name
1704.04309.pdf
Description
Submitted version
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559.38 KB
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Checksum (MD5)
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Author(s)
Barraquand, Guillaume
Borodin, Alexei
Corwin, Ivan
Wheeler, Michael
Date Issued
August 27, 2018
Journal
Duke Mathematical Journal
Publisher
Duke University Press
Citation
Barraquand, Guillaume et al. "Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process." Duke Mathematical Journal, 167, 13 (August 2018): 2457--2529.
Version
Original manuscript
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 τ) according to the Tracy–Widom Gaussian orthogonal ensemble distribution on the τ[superscript 1/3]-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. Keywords: Kardar–Parisi–Zhang universality class; interacting particle systems; asymmetric simple exclusion process; six-vertex model; integrable probability; Macdonald symmetric functions; Yang–Baxter equation
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1215/00127094-2018-0019
