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Limit Shapes of the Stochastic Six Vertex Model

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Abstract

It is shown that limit shapes for the stochastic 6-vertex model on a cylinder with the uniform boundary state on one end are solutions to the Burger type equation. Solutions to these equations are studied for step initial conditions. When the circumference goes to infinity the solution corresponding to critical initial densities coincides with the one found by Borodin, Corwin, and Gorin.

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Acknowledgements

We would like to thank D.Keating formany helpful discussions and for running numerical simulations. Both authors were supported by the NSF Grant DMS-1201391. The work of A. S. was supported by RTG NSF Grant 30550. We are grateful for the hospitality at Universite Paris VII. The research of N. R. was partly supported by the Russian Science Foundation (Project No. 14-11-00598). He also would like to thank QGM center at the University of Aarhus for hospitality. Lastly, we thank the anonymous reviewer for many helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Nicolai Reshetikhin

  2. KdV Institute for Mathematics, University of Amsterdam, 1098 XH, Amsterdam, The Netherlands

    Nicolai Reshetikhin

  3. ITMO University, Saint Petersburg, Russia, 197101

    Nicolai Reshetikhin

  4. Department of Physics, University of California, Berkeley, CA, 94720, USA

    Ananth Sridhar

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  1. Nicolai Reshetikhin
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  2. Ananth Sridhar
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Correspondence to Nicolai Reshetikhin.

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Communicated by H.-T. Yau

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Reshetikhin, N., Sridhar, A. Limit Shapes of the Stochastic Six Vertex Model. Commun. Math. Phys. 363, 741–765 (2018). https://doi.org/10.1007/s00220-018-3253-2

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