Stochastic six-vertex model
Name
Borodin_Stochastic six.pdf
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582.28 KB
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Checksum (MD5)
6c57360c0ae559bd0a8b2ed6d6a69a6a
Author(s)
Borodin, Alexei
Corwin, Ivan
Gorin, Vadim
Date Issued
November 2015
Journal
Duke Mathematical Journal
Publisher
Duke University Press
Citation
Borodin, Alexei; Corwin, Ivan and Gorin, Vadim. “Stochastic Six-Vertex Model.” Duke Mathematical Journal 165, 3 (February 2016): 563–624
Version
Original manuscript
Abstract
We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit shape as the mesh size tends to 0. We further prove that the one-point fluctuations around the limit shape are asymptotically governed by the GUE Tracy–Widom distribution. We also explain an equivalent formulation of our model as an interacting particle system, which can be viewed as a discrete time generalization of ASEP started from the step initial condition. Our results confirm a 1992 prediction of Gwa and Spohn that this system belongs to the KPZ universality class.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1215/00127094-3166843
